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100 | Higgs line bundles, Green-Lazarsfeld sets,and maps of Kähler manifolds to curves | math.AG | Let $X$ be a compact K\"ahler manifold. The set $\cha(X)$ of one-dimensional
complex valued characters of the fundamental group of $X$ forms an algebraic
group. Consider the subset of $\cha(X)$ consisting of those characters for
which the corresponding local system has nontrivial cohomology in a given
degree $d$. This ... | math |
101 | A theory of algebraic cocycles | math.AG | We introduce the notion of an algebraic cocycle as the algebraic analogue of
a map to an Eilenberg-MacLane space. Using these cocycles we develop a
``cohomology theory" for complex algebraic varieties. The theory is bigraded,
functorial, and admits Gysin maps. It carries a natural cup product and a
pairing to $L$-homol... | math |
102 | Zariski Geometries | math.AG | We characterize the Zariski topologies over an algebraically closed field in
terms of general dimension-theoretic properties. Some applications are given to
complex manifold and to strongly minimal sets. | math |
103 | Configuration spaces and the space of rational curves on a toric variety | math.AG | The space of holomorphic maps from $S^2$ to a complex algebraic variety $X$,
i.e. the space of parametrized rational curves on $X$, arises in several areas
of geometry. It is a well known problem to determine an integer $n(D)$ such
that the inclusion of this space in the corresponding space of continuous maps
induces i... | math |
104 | Stable vector bundles on algebraic surfaces | math.AG | We prove an existence result for stable vector bundles with arbitrary rank on
an algebraic surface, and determine the birational structure of certain moduli
space of stable bundles on a rational ruled surface. | math |
105 | Toric Intersection Theory for Affine Root Counting | math.AG | Given any polynomial system with fixed monomial term structure, we give
explicit formulae for the generic number of roots with specified coordinate
vanishing restrictions. For the case of affine space minus an arbitrary union
of coordinate hyperplanes, these formulae are also the tightest possible upper
bounds on the n... | math |
106 | On Hyper Kähler manifolds associated to Lagrangean Kähler submanifolds of $T^*{\Bbb C}^n$ | math.AG | For any Lagrangean K\"ahler submanifold $M \subset T^*{\Bbb C}^n$, there
exists a canonical hyper K\"ahler metric on $T^*M$. A K\"ahler potential for
this metric is given by the generalized Calabi Ansatz of the theoretical
physicists Cecotti, Ferrara and Girardello. This correspondence provides a
method for the constru... | math |
107 | Rational curves and ampleness properties of the tangent bundle of algebraic varieties | math.AG | The purpose of this paper is to translate positivity properties of the
tangent bundle (and the anti-canonical bundle) of an algebraic manifold into
existence and movability properties of rational curves and to investigate the
impact on the global geometry of the manifold $X$. Among the results we prove
are these:
\qu... | math |
108 | Quantum cohomology of projective bundles over P^n | math.AG | In this paper, we attempt to determine the quantum cohomology of projective
bundles over the projective space P^n. In contrast to the previous examples,
the relevant moduli spaces in our case frequently do not have expected
dimensions. It makes the calculation more difficult. We overcome this
difficulty by using excess... | math |
109 | Extensions of vector bundles and rationality of certain moduli spaces of stable bundles | math.AG | In this paper, it is proved that certain stable rank-3 vector bundles can be
written as extensions of line bundles and stable rank-2 bundles. As an
application, we show the rationality of certain moduli spaces of stable rank-3
bundles over the projective plane P^2. | math |
110 | Rank-3 stable bundles on rational ruled surfaces | math.AG | In this paper, we compare the moduli spaces of rank-3 vector bundles stable
with respect to different ample divisors over rational ruled surfaces. We also
discuss the irreducibility, unirationality, and rationality of these moduli
spaces. | math |
111 | Topological arrangement of curves of degree 6 on cubic surfaces in $\Bbb R P^3$ | math.AG | A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R
P^3$. The papers classifies the nonsingular curves cut in this way on
non-singular cubic surfaces up to homeomorphism.
Two issues new in the study related to the first part of the 16th Hilbert
problem appear in this classification. One is the di... | math |
112 | Adjunction inequality for real algebraic curves | math.AG | The zero set of a real polynomial in two variable is a curve in $\mathbb
R^2$. For a generic choice of its coefficients this is a non-singular curve, a
collection of circles and lines properly embedded in $\mathbb R^2$. What
topological arrangements of these circles and lines appear for the polynomials
of a given degre... | math |
113 | Subspace Arrangements over Finite Fields: Cohomological and Enumerative Properties | math.AG | The enumeration of points on (or off) the union of some linear or affine
subspaces over a finite field is dealt with in combinatorics via the
characteristic polynomial and in algebraic geometry via the zeta function. We
discuss the basic relations between these two points of view. Counting points
is also related to the... | math |
114 | On Rigidity and the Albanese Variety for Parallelizable Manifolds | math.AG | We study the rigidity questions and the Albanese Variety for Complex
Parallelizable Manifolds. Both are related to the study of the cohomology group
$H^1(X,\mathcal O)$. In particular we show that a compact complex
parallelizable manifold is rigid iff $b_1(X)=0$ iff Alb$(X)=\{e\}$ iff
$H^1(X,\mathcal O)=0$. | math |
115 | Flat Vector Bundles over Parallelizable Manifolds | math.AG | We study flat vector bundles over complex parallelizable manifolds. | math |
116 | Pieri-type formulas for maximal isotropic Grassmannains via triple intersections | math.AG | We give an elementary proof of the Pieri-type formula in the cohomology of a
Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic
vector space. This proof proceeds by explicitly computing a triple intersection
of Schubert varieties. The decisive step is an exact description of the
intersection... | math |
117 | On quantum cohomology rings of partial flag varieties | math.AG | The main goal of this paper is to give a unified description for the
structure of the small quantum cohomology rings for all homogeneous spaces of
SL_n(C). | math |
118 | A conjectural description of the tautological ring of the moduli space of curves | math.AG | The purpose of this paper is to formulate a number of conjectures giving a
rather complete description of the tautological ring of M_g and to discuss the
evidence for these conjectures. | math |
119 | A non-vanishing result for the tautological ring of {\cal M}_g | math.AG | Looijenga recently proved that the tautological ring of M_g vanishes in
degree d>g-2 and is at most one-dimensional in degree g-2, generated by the
class of the hyperelliptic locus. Here we show that K_{g-2} is non-zero on M_g.
The proof uses the Witten conjecture, proven by Kontsevich. With similar
methods, we expect ... | math |
120 | Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0 | math.AG | Let $V$ be a smooth, projective, convex variety. We define tautological
$\psi$ and $\kappa$ classes on the moduli space of stable maps $\M_{0,n}(V)$,
give a (graphical) presentation for these classes in terms of boundary strata,
derive differential equations for the generating functions of the Gromov-Witten
invariants ... | math |
121 | Germs of de Rham cohomology classes which vanish at the generic point | math.AG | We show that hypergeometric differential equations, unitary and Gauss-Manin
connections give rise to de Rham cohomology sheaves which do not admit a
Bloch-Ogus resolution. The latter is in contrast to Panin's theorem asserting
that corresponding \'etale cohomology sheaves do fulfill Bloch-Ogus theory. | math |
122 | K. Saito's Duality for Regular Weight Systems and Duality for Orbifoldized Poincare Polynomials | math.AG | We will show that the duality for regular weight systems introduced by K.
Saito can be interpreted as the duality for orbifoldized Poincare polynomials. | math |
123 | Characteristic varieties of algebraic curves | math.AG | We study tori attached to the fundamental groups of plane curves with
arbitrary singularities. These tori provide complete information about homology
of finite abelian covers of the plane branched along the curve. We calculate
these tori in terms of certain linear systems determined by the singularities
of the curve. I... | math |
124 | Lectures on Exotic Algebraic Structures on Affine Spaces | math.AG | These notes are based on the lecture courses given at the
Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul
Sabatier (Toulouse, 08-12.01.1996). | math |
125 | Affine modifications and affine hypersurfaces with a very transitive automorphism group | math.AG | We study a kind of modification of an affine domain which produces another
affine domain. First appeared in passing in the basic paper of O. Zariski
(1942), it was further considered by E.D. Davis (1967). The first named author
applied its geometric counterpart to construct contractible smooth affine
varieties non-isom... | math |
126 | The local monodromy as a generalized algebraic correspondence | math.AG | In the paper we show that for a normal-crossings degeneration $Z$ over the
ring of integers of a local field with $X$ as generic fibre, the local
monodromy operator and its powers determine invariant cocycle classes under the
decomposition group in the cohomology of the product $X \times X$. More
precisely, they also d... | math |
127 | Algebraic theory of characteristic classes of bundles with connection | math.AG | This is a survey on the topic explained in the title, for the proceedings on
the K-theory 1997 summer institute in Seattle. | math |
128 | The Pfaffian Calabi-Yau, its Mirror, and their link to the Grassmannian G(2,7) | math.AG | The rank 4 locus of a general skew-symmetric 7x7 matrix gives the pfaffian
variety in P^20 which is not defined as a complete intersection. Intersecting
this with a general P^6 gives a Calabi-Yau manifold. An orbifold construction
seems to give the 1-parameter mirror-family of this. However, corresponding to
two points... | math |
129 | On the zeta-function of a polynomial at infinity | math.AG | We use the notion of Milnor fibres of the germ of a meromorphic function and
the method of partial resolutions for a study of topology of a polynomial map
at infinity (mainly for calculation of the zeta-function of a monodromy). It
gives effective methods of computation of the zeta-function for a number of
cases and a ... | math |
130 | Characteristic Classes of Hypersurfaces and Characteristic Cycles | math.AG | We give a new formula for the Chern-Schwartz-MacPherson class of a
hypersurface in a nonsigular compact complex analytic variety. In particular
this formula generalizes our previous result on the Euler characteristic of
such a hypersurface. Two different approaches are presented. The first is based
on the theory of cha... | math |
131 | On maximal curves having classical Weierstrass gaps | math.AG | We study geometrical properties of maximal curves having classical
Weierstrass gaps. | math |
132 | Preuve d'une conjecture de Frenkel-Gaitsgory-Kazhdan-Vilonen | math.AG | We prove a conjecture of Frenkel-Gaitsgory-Kazhdan-Vilonen on some
exponential sums related to the geometric Langlands correspondence. Our main
ingredients are the resolution of Lusztig scheme of lattices introduced by
Laumon and the decomposition theorem of Beilinson-Bernstein-Deligne-Gabber. | math |
133 | Varieties of sums of powers | math.AG | The variety of sums of powers of a homogeneous polynomial of degree d in n
variables is defined and investigated in some examples, old and new. These
varieties are studied via apolarity and syzygies. Classical results of
Sylvester (1851), Hilbert (1888), Dixon and Stuart (1906) and some more recent
results of Mukai (19... | math |
134 | A Base Point Free Theorem of Reid Type, II | math.AG | Let $X$ be a complete algebraic variety over {\bf C}. We consider a log
variety $(X,\Delta)$ that is weakly Kawamata log terminal. We assume that
$K_X+\Delta$ is a {\bf Q}-Cartier {\bf Q}-divisor and that every irreducible
component of $\lfloor \Delta \rfloor$ is {\bf Q}-Cartier. A nef and big Cartier
divisor $H$ on $X... | math |
135 | An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation | math.AG | We give an algorithm to compute the following cohomology groups on $U = \C^n
\setminus V(f)$ for any non-zero polynomial $f \in \Q[x_1, ..., x_n]$; 1.
$H^k(U, \C_U)$, $\C_U$ is the constant sheaf on $U$ with stalk $\C$. 2. $H^k(U,
\Vsc)$, $\Vsc$ is a locally constant sheaf of rank 1 on $U$. We also give
partial results... | math |
136 | Degeneration of curves and analytic deformation | math.AG | Let C_1 and C_2 be two degenerations of genus g curves. We prove that if two
degenerations defines the same conjugacy classes in the mapping class group,
they are equivalent under analytic deformations. | math |
137 | Singularities | math.AG | This article recounts the interaction of topology and singularity theory
(mainly singularities of complex algebraic varieties) which started in the
early part of this century and bloomed in the 1960's with the work of
Hirzebruch, Brieskorn, Milnor and others. Some of the topics are followed to
the present day. (A chapt... | math |
138 | Vector bundles on G(1,4) without intermediate cohomology | math.AG | We characterize the vector bundles on G(1,4) that have no intermediate
cohomology. We obtain them from extensions of the universal bundles and others
related with them. In particular, we get a characterization of the universal
vector bundles from their cohomology. | math |
139 | Non-resonance D-modules over arrangements of hyperplanes | math.AG | The aim of this note is a combinatorial description of a category of
$D$-modules over an affine space, smooth along the stratification defined by an
arrangement of hyperplanes. These $D$-modules are assumed to satisfy certain
non-resonance condition. The main result, see Theorem 4.1, generalizes
[S.Khoroshkin, $D$-modu... | math |
140 | Grassmannian of $k((z))$: Picard Group, Equations and Automorphisms | math.AG | This paper aims at generalizing some geometric properties of Grassmannians of
finite dimensional vector spaces to the case of Grassmannnians of infinite
dimensional ones, in particular for that of $k((z))$. It is shown that the
Determinant Line Bundle generates its Picard Group and that the Pl\"ucker
equations define i... | math |
141 | Remarks on formal deformations and Batalin-Vilkovisky algebras | math.AG | This note consists of two parts. Part I is an exposition of (a part of) the
V.Drinfeld's letter, [D].
The sheaf of algebras of polyvector fields on a Calabi-Yau manifold, equipped
with the Schouten bracket, admits a structure of a Batalin-Vilkovisky algebra.
This fact was probably first noticed by Z.Ran, [R]. Part II... | math |
142 | On the Severi varieties of surfaces in P^3 | math.AG | The Severi variety V_{n,d} of a smooth projective surface S is defined as the
subvariety of the linear system |O_S(n)|, which parametrizes curves with d
nodes. We show that, for a general surface S of degree k in P^3 and for all
n>k-1, d=0,...,dim(|O_S(n)|), there exists one component of V_{n,d} which is
reduced, of th... | math |
143 | Castelnuovo regularity for smooth projective varieties of dimensions 3 and 4 | math.AG | Castelnuovo-Mumford regularity is an important invariant of projective
algebraic varieties. A well known conjecture due to Eisenbud and Goto gives a
bound for regularity in terms of the codimension and degree. This conjecture is
known to be true for curves (Gruson-Lazarsfeld-Peskine) and smooth surfaces
(Pinkham, Lazar... | math |
144 | Castelnuovo-Mumford Regularity of Smoth Threefolds in P^5 | math.AG | Castelnuovo-Mumford regularity is an important invariant of projective
algebraic varieties. A well known conjecture due to Eisenbud and Goto gives a
bound for regularity in terms of the codimension and degree,i.e.,
Castelnuovo-Mumford regularity of a given variety $X$ is less than or equal to
$deg(X)-codim(X)+1$. This ... | math |
145 | Varietes de modules alternatives | math.AG | Let X be a projective irreducible smooth algebraic variety. A "fine moduli
space" of sheaves on X is a family F of coherent sheaves on X parametrized by
an integral variety M such that : F is flat on M; for all distinct points x, y
of M the sheaves F_x, F_y on X are not isomorphic and F is a complete
deformation of F_x... | math |
146 | Rational Curves on the Space of Determinantal Nets of Conics | math.AG | We describe the Hilbert scheme components parametrizing lines and conics on
the space of determinantal nets of conics, N. As an application, we use the
quantum Lefschetz hyperplane principle to compute the instanton numbers of
rational curves on a complete intersection Calabi-Yau threefold in N. We also
compute the num... | math |
147 | Noncommutative geometry based on commutator expansions | math.AG | We develop an approach to noncommutative algebraic geometry ``in the
perturbative regime" around ordinary commutative geometry. Let R be a
noncommutative algebra and A=R/[R,R] its commutativization. We describe what
should be the formal neighborhood of M=Spec(A) in the (nonexistent) space
Spec(R). This is a ringed spac... | math |
148 | Index 1 covers of log terminal surface sigularities | math.AG | We shall investigate index 1 covers of 2-dimensional log terminal
singularities. The main result is that the index 1 cover is canonical if the
characteristic of the base field is different from 2 or 3. We also give some
counterexamples in the case of characteristic 2 or 3. By using this result, we
correct an error in a... | math |
149 | Monodromy weight filtration is independent of l | math.AG | In this paper, we prove the l-independence of monodromy weight filtration for
a geometrically smooth variety over an equicharacteristic local field. We also
prove the l-independence for the geometric monodromy representation on the
associated graded module of weight monodromy filtration. | math |
150 | Real Algebraic Threefolds III: Conic Bundles | math.AG | This is the third of a series of papers studying real algebraic threefolds,
but the methods are mostly independent from the previous two. Let $f:X\to S$ be
a map of a smooth projective real algebraic 3-fold to a surface $S$ whose
general fibers are rational curves.
Assume that the set of real points of $X$ is an orie... | math |
151 | Primitive Forms, Topological LG models coupled to Gravity and Mirror Symmetry | math.AG | In this paper, we will describe the mathematical foundation of topological
Landau-Ginzburg (LG) models coupled to gravity at genus 0 in terms of primitive
forms. We also discuss the mirror symmetry for Calabi-Yau manifolds and CP^1 in
our context. We will show that the mirror partner of CP^1 is the theory of
primitive ... | math |
152 | Equivariant cohomology and equivariant intersection theory | math.AG | This text is an introduction to equivariant cohomology, a classical tool for
topological transformation groups, and to equivariant intersection theory, a
much more recent topic initiated by D. Edidin and W. Graham. It is based on
lectures given at Montr\'eal is Summer 1997.
Our main aim is to obtain explicit descript... | math |
153 | A set on which the Lojasieewicz exponent at infinity is attained | math.AG | We show that for a polynomial mapping F = (f_1,...,f_m): C^n \to C^m the
Lojasiewicz exponent at infinity of F is attained on the set {z \in C^n :
f_1(z)...f_m(z) = 0} | math |
154 | Algebraic monoids and group embeddings | math.AG | We study the geometry of algebraic monoids. We prove that the group of
invertible elements of an irreducible algebraic monoid is an algebraic group,
open in the monoid. Moreover, if this group is reductive, then the monoid is
affine. We then give a combinatorial classification of reductive monoids by
means of the theor... | math |
155 | On the Moduli space of diffeomorphic algebraic surfaces | math.AG | It is proved that the number of deformation types of complex structures on a
fixed oriented smooth four-manifold can be arbitrarily large. The considered
examples are locally simple abelian covers of rational surfaces. | math |
156 | Boundedness of semistable principal bundles on a curve, with classical semisimple structure groups | math.AG | In characteristic zero, semistable principal bundles on a nonsingular
projective curve with a semisimple structure group form a bounded family, as
shown by Ramanathan in 1970's using the Narasimhan-Seshadri theorem. This was
the first step in his construction of moduli for principal bundles. In this
paper we prove boun... | math |
157 | The Chow ring of a classifying space | math.AG | We define the Chow ring of the classifying space of a linear algebraic group.
In all the examples where we can compute it, such as the symmetric groups and
the orthogonal groups, it is isomorphic to a natural quotient of the complex
cobordism ring of the classifying space, a topological invariant. We apply this
to get ... | math |
158 | A note on k-jet ampleness on surfaces | math.AG | We prove Reider type criterions for k-jet spannedness and k-jet ampleness of
adjoint bundles for surfaces with at most rational singularities. Moreover, we
prove that on smooth surfaces [n(n+4)/4]-very ampleness implies n-jet
ampleness. | math |
159 | Pluricanonical systems on surfaces with small K^2 | math.AG | We prove that the bicanonical system on a surface of general type with K^2=4
has no base components and describe clusters contracted by 4K_X for a numerical
Godeaux surface and 3K_X for a numerical Campedelli surface. | math |
160 | On plane maximal curves | math.AG | The genus of a maximal curve over a finite field with r^2 elements is either
g_0=r(r-1)/2 or less than or equal to g_1=(r-1)^2/4. Maximal curves with genus
g_0 or g_1 have been characterized up to isomorphism. A natural genus to be
studied is g_2=(r-1)(r-3)/8, and for this genus there are two non-isomorphism
maximal cu... | math |
161 | Mori conic bundles with a reduced log terminal boundary | math.AG | We study the local structure of Mori contractions $f\colon X\to Z$ of
relative dimension one under an additional assumption that there exists a
reduced divisor $S$ such that $K_X+S$ is plt and anti-ample. | math |
162 | Effectivity of Arakelov divisors and the theta divisor of a number field | math.AG | We introduce the notion of an effective Arakelov divisor for a number field
and the arithmetical analogue of the dimension of the space of sections of a
line bundle. We study the analogue of the theta divisor for a number field. | math |
163 | Calculating cohomology groups of moduli spaces of curves via algebraic geometry | math.AG | We compute the first, second, third, and fifth rational cohomology groups of
the moduli space of stable n-pointed genus g curves, for all g and n, using
(mostly) algebro-geometric techniques. | math |
164 | Enumerative geometry of plane curves of low genus | math.AG | We collect various known results (about plane curves and the moduli space of
stable maps) to derive new recursive formulas enumerating low genus plane
curves of any degree with various behaviors. Recursive formulas are given for
the characteristic numbers of rational plane curves, elliptic plane curves, and
elliptic pl... | math |
165 | Cohomological invariants of complex manifolds coming from extremal rays | math.AG | In the present paper Mori extremal rays of a smooth projective manifold X are
divided into two classes: L-supported and L-negligible (where ``L'' stands for
``Lefschetz'' since the division comes from Hard Lefschetz Theorem). Roughly
speaking: L-supported rays are strongly distinguishable in topology while
L-negligible... | math |
166 | Singularities of 2theta-divisors in the Jacobian | math.AG | We study several subseries of the space of second order theta functions on
the Jacobian of a non-hyperelliptic curve. In particular, we are interested in
the subseries P\Gamma_{00} consisting of 2theta-divisors having multiplicity at
least 4 at the origin, or, equivalently, containing the surface C-C, and in its
analog... | math |
167 | Massey and Fukaya products on elliptic curves | math.AG | This note is a continuation of our paper with E. Zaslow "Categorical mirror
symmetry: the elliptic curve", math.AG/9801119. We compare some triple Massey
products on elliptic curve with the corresponding Fukaya products on the
symplectic torus and recover the classical identity due to Kronecker. We also
compute some tr... | math |
168 | Locally symmetric families of curves and jacobians | math.AG | This paper addresses the following question of Oort: "Are there any postive
dimensional locally symmetric subvarieties of the moduli space of abelian
varieties that are contained in the jacobian locus and contain the jacobian of
at least one smooth curve? Some partial results are given. | math |
169 | On curves covered by the Hermitian curve | math.AG | For each proper divisor d of (r^2-r+1), r being a power of a prime, maximal
curves over a finite field with r^2 elements covered by the Hermitian curve of
genus 1/2((r^2-r+1)/d-1) are constructed. | math |
170 | Character sums associated to finite Coxeter groups | math.AG | We prove a character sum identity for Coxeter arrangements which is a finite
field analogue of Macdonald's conjecture proved by Opdam. | math |
171 | Germs of arcs on singular algebraic varieties and motivic integration | math.AG | We study the scheme of formal arcs on a singular algebraic variety and its
images under truncations. We prove a rationality result for the Poincare series
of these images which is an analogue of the rationality of the Poincare series
associated to p-adic points on a p-adic variety. The main tools which are used
are sem... | math |
172 | Motivic Igusa zeta functions | math.AG | We define motivic analogues of Igusa's local zeta functions. These functions
take their values in a Grothendieck group of Chow motives. They specialize to
p-adic Igusa local zeta functions and to the topological zeta functions we
introduced several years ago. We study their basic properties, such as
functional equation... | math |
173 | Chiral de Rham complex | math.AG | The aim of this note is to define certain sheaves of vertex algebras on
smooth manifolds. For each smooth complex algebraic (or analytic) manifold $X$,
we construct a sheaf $\Omega^{ch}_X$, called the {\bf chiral de Rham complex}
of $X$. It is a sheaf of vertex algebras in the Zarisky (or classical)
topology, It comes ... | math |
174 | On $-K^2$ for normal surface singularities | math.AG | In this paper we show the lower bound of the set of non-zero $-K^2$ for
normal surface singularities establishing that this set has no accumulation
points from above. We also prove that every accumulation point from below is a
rational number and every positive integer is an accumulation point. Every
rational number ca... | math |
175 | Motivic exponential integrals and a motivic Thom-Sebastiani Theorem | math.AG | We introduce motivic analogues of p-adic exponential integrals. We prove a
basic multiplicativity property from which we deduce a motivic analogue of the
Thom-Sebastiani Theorem. In particular, we obtain a new proof of the
Thom-Sebastiani Theorem for the Hodge spectrum of (non isolated) singularities
of functions. | math |
176 | Elliptic Gromov - Witten invariants and the generalized mirror conjecture | math.AG | A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic
terms of semi-simple Frobenius structures and complex oscillating integrals is
formulated. The proof of the conjecture is given for torus-equivariant Gromov -
Witten invariants of compact K\"ahler manifolds with isolated fixed points and
for c... | math |
177 | Intersection pairing for arithmetic cycles with degenerate Green currents | math.AG | In this note, we would like to propose a suitable extension of the arithmetic
Chow group of codimension one, in which the Hodge index theorem holds. We also
prove an arithmetic analogue of Bogomolov's instability theorem for rank 2
vector bundles on arbitrary regular projective arithmetic varieties. | math |
178 | Ray class fields of global function fields with many rational places | math.AG | A general type of ray class fields of global function fields is investigated.
The systematic computation of their genera leads to new examples of curves over
finite fields with comparatively many rational points. | math |
179 | Strange duality and polar duality | math.AG | We describe a relation between Arnold's strange duality and a polar duality
between the Newton polytopes which is mostly due to M.~Kobayashi. We show that
this relation continues to hold for the extension of Arnold's strange duality
found by C.~T.~C.~Wall and the author. By a method of Ehlers-Varchenko, the
characteris... | math |
180 | Poisson structures on algebraic threefolds | math.AG | The aim of this paper is to find all algebraic threefolds admitting
quasi-regular Poisson structure. There are three types of such varieties:
abelian varieties, smooth flat conic bundles over abelian surfaces and
quotients of the product of a curve and a symplectic surface by a finite group. | math |
181 | Riemann-Roch Theorems for Deligne-Mumford Stacks | math.AG | The goal of this paper is to prove Riemann-Roch type theorems for
Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with
coefficients in representations" and a Chern character, and we prove a
Grothendieck-Riemann-Roch theorem for the Riemann-Roch transformation it
defines. As a corollary we obta... | math |
182 | Chern Classes of Tautological Sheaves on Hilbert Schemes | math.AG | We give an algorithmic description of the action of the Chern classes of
tautological bundles on the cohomology of Hilbert schemes of points on surfaces
within the framework of Nakajima's oscillator algebra. This leads to an
identification of the cohomology ring of Hilbert schemes of the affine plane
with a ring of dif... | math |
183 | On a series of Gorenstein cyclic quotient singularities admitting a unique projective crepant resolution | math.AG | In this paper we prove that the Gorenstein cyclic quotient singularities of
type \frac 1l (1,..., 1,l-(r-1)) with $l\geq r\geq 2$, have a
\textit{unique}torus-equivariant projective, crepant, partial resolution, which
is ``full'' iff either $l\equiv 0$ mod $% (r-1) $ or $l\equiv 1$ mod $(r-1) $.
As it turns out, if one... | math |
184 | On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities | math.AG | An immediate generalization of the classical McKay correspondence for
Gorenstein quotient spaces $\Bbb{C}^{r}/G$ in dimensions $r\geq 4$ would
primarily demand the existence of projective, crepant, full desingularizations.
Since this is not always possible, it is natural to ask about special classes
of such quotient sp... | math |
185 | On a conjecture of Le Bruyn | math.AG | Given a generic field extension F/k of degree n>3 (i.e. the Galois group of
the normal closure of F is isomorphic to the symmetric group $S_n$), we prove
that the norm torus, defined as the kernel of the norm map
$N:R_{F/k}(G_m)\to\G_m$, is not rational over k. | math |
186 | Mirror Symmetry and Toric Degenerations of Partial Flag Manifolds | math.AG | In this paper we propose and discuss a mirror construction for complete
intersections in partial flag manifolds $F(n_1, ..., n_l, n)$. This
construction includes our previous mirror construction for complete
intersection in Grassmannians and the mirror construction of Givental for
complete flag manifolds. The key idea ... | math |
187 | Triades et familles de courbes gauches | math.AG | Let $A$ be a noetherian ring and $R_A$ be the graded ring $A[X,Y,Z,T]$. In
this article we introduce the notion of a triad, which is a generalization to
families of curves in ${\bf P}^3_A$ of the notion of Rao module. A triad is a
complex of graded $R_A$-modules $(L_1 \to L_0 \to L_{-1})$ with certain
finiteness hypoth... | math |
188 | Albanese and Picard 1-motives | math.AG | We define, in a purely algebraic way, 1-motives $Alb^{+}(X)$, $Alb^{-}(X)$,
$Pic^{+}(X)$ and $Pic^{-}(X)$ associated with any algebraic scheme $X$ over an
algebraically closed field of characteristic zero. For $X$ over $\C$ of
dimension $n$ the Hodge realizations are, respectively, $H^{2n-1}(X)(n)$,
$H_{1}(X)$, $H^{1}(... | math |
189 | Chern classes and the periods of mirrors | math.AG | We show how Chern classes of a Calabi Yau hypersurface in a toric Fano
manifold can be expressed in terms of the holomorphic at a maximal degeneracy
point period of its mirror. We also consider the relation between Chern classes
and the periods of mirrors for complete intersections in Grassmanian Gr(2,5). | math |
190 | A note on the symplectic structure on the space of G-monopoles | math.AG | Let $G$ be a semisimple complex Lie group with a Borel subgroup $B$. Let
$X=G/B$ be the flag manifold of $G$. Let $C=P^1\ni\infty$ be the projective
line. Let $\alpha\in H_2(X,{\Bbb Z})$. The moduli space of $G$-monopoles of
topological charge $\alpha$ (see e.g. [Jarvis]) is naturally identified with
the space $M_b(X,\... | math |
191 | A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension | math.AG | The recent two proofs for the (weak) factorization theorem for birational
maps, one by W{\l}odarczyk and the other by
Abramovich-Karu-Matsuki-W{\l}odarczyk rely on the results of Morelli. The
former uses the process for $\pi$-desingularization (the most subtle part of
Morelli's combinatorial algorithm), while the latte... | math |
192 | Jacobian Conjecture and Nilpotent Mappings | math.AG | We prove the equivalence of the Jacobian Conjecture (JC(n)) and the
Conjecture on the cardinality of the set of fixed points of a polynomial
nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n). | math |
193 | On a Chisini Conjecture | math.AG | Chisini's conjecture asserts that for a cuspidal curve $B\subset \mathbb P^2$
a generic morphism $f$ of a smooth projective surface onto $\mathbb P^2$ of
degree $\geq 5$, branched along $B$, is unique up to isomorphism. We prove that
if $\deg f$ is greater than the value of some function depending on the degree,
genus,... | math |
194 | 3-fold log flips according to V.V.Shokurov | math.AG | In this paper, I review the section 8 of V.V.Shokurov's paper '3-fold log
flips'. | math |
195 | On the minimal free resolution of non-special curves in P^3 | math.AG | Here we prove that the minimal free resolution of a general space curve of
large degree (e.g. a general space curve of degree d and genus g with d g+3,
except for finitely many pairs (d,g)) is the expected one. A similar result
holds even for general curves with special hyperplane section and, roughly, d
g/2. The proof... | math |
196 | Chow quotients and projective bundle formulas for Euler-Chow series | math.AG | Given a projective algebraic variety $X$, let $\Pi_p(X)$ denote the monoid of
effective algebraic equivalence classes of effective algebraic cycles on $X$.
The $p$-th Euler-Chow series of $X$ is an element in the formal monoid-ring
$Z[[\Pi_p(X)]]$ defined in terms of Euler characteristics of the Chow varieties
$\cvpd{p... | math |
197 | Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et Ye | math.AG | We give a geometric interpretation of the base change homomorphism between
the Hecke algebra of GL(n) for an unramified extension of local fields of
positive characteristic. For this, we use some results of Ginzburg, Mirkovic
and Vilonen related to the geometric Satake isomorphism. We give new proof for
these results i... | math |
198 | Linear Systems of Plane Curves with Base Points of Equal Multiplicity | math.AG | In this article we address the problem of computing the dimension of the
space of plane curves of degree $d$ with $n$ general points of multiplicity
$m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$,
the dimension is equal to the expected dimension given by the Riemann-Roch
Theorem. Also, sys... | math |
199 | Vector bundles on Fano 3-folds without intermediate cohomology | math.AG | We study the vector bundles without intermediate cohomology on Fano
threefolds of index two, degree d=3,4,5 and Betti number one. We obtain a
complete characterization in the case of rank-two vector bundles. For arbitrary
rank, we give all possible Chern classes of such vector bundles, under some
general condition. | math |
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