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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements quadratic form; quasilinear quadratic form; quasi-Pfister form; quasi-Pfister neighbor; isotropy; isotropy index; function field of a quadric
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements ordered basis; homogeneous root system; reflections; quasi-Coxeter elements; braid group; monodromy
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements quantum statistical model; \(C^*\)-dynamical system; commensurable class of \(Q\)-lattice; KMS state; Type \(\text{II}_1\)-factor; modular field; Eisenstein series A. Connes and M. Marcolli, ''From physics to number theory v...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements index of regularity; Hilbert function; plurigenera; number of integral points; Newton polyhedra; resolution; complete intersection singularity Marcel Morales, Resolution of quasihomogeneous singularities and plurigenera, Com...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements elliptic curves with complex multiplication; elliptic curves over an imaginary quadratic field; Iwasawa theory; supersingular primes; Schneider-Greenberg conjecture; \(p^ m\)-torsion subgroups; \(\mathbb{Z}_ p\)-cyclotomic e...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements invariants preserving transformations; determinant; trace; rank; R-linear transformations; survey article; Picard group; R-submodules; group schemes; exact sequence in non-abelian cohomology
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements flag varieties; line bundles; integrable systems; Darboux transformations; Miura transform; integrable deformations; linear systems
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements \(K3\) surface, double cover family of \(K3\) surfaces, period, mirror map, \(K3\) lambda function, hypergeometric system, mirror symmetry
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements fat point; Hilbert function; minimal number of homogeneous generators; minimal free resolution
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements orthogonal groups; moduli space of hyperelliptic curves; Plücker morphism R. Sasaki, Moduli space of hyperelliptic curves of genus two with level \((2,4)\) structure and the special orthogonal group of degree three, Kyushu J...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements fully commutative elements; nilpotent orbits; ad-nilpotent ideals of Borel subalgebras
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements lower bound; logarithms of algebraic points on an algebraic group; simultaneous independent linear forms Hirata-Kohno, N.: Approximations simultanées sur LES groupes algébriques commutatifs. Compositio math. 86, 9-96 (1993)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Fano-Mori fibre space; birational rigidity; maximal singularity; hypertangent divisor; log canonical singularity; linear system; canonical class Pukhlikov, A. V., Birationally rigid Fano fibrations. II, Izv. Ross. Akad. Nauk...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements fat points; line arrangements; linear systems; splitting types of vector bundles
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements cohomology groups; complete linear system; monoidal transformation; Picard group; rational surface
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Fano manifolds; families of lines; covered by linear spaces
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements characteristic p; system of parameters; d-sequence; Buchsbaum ring; finite local cohomology Goto, S., Ogawa, T.: A Note on Rings with Finite Local Cohomology. Tokyo J. Math.6, 403--411 (1983)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements analysis and modelling of signals; discrete linear stochastic signals; estimation algebras; Grassmannian representations of matrix transfer functions
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Weierstrass point; Brill-Noether theory; Kodaira dimension; degenerations; smoothings of linear series; moduli space of curves of genus g; monodromy group Eisenbud, D., Harris, J.: The irreducibility of some families of line...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements equisingular families of curves; prescribed singularities; fat points schemes Keilen, T.: Reducible families of curves with ordinary multiple points on surfaces in projective three-space, Comm. in algebra 34,5, 1921-1926 (20...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements local uniformization; resolution of singularities Knaf H. and Kuhlmann F.-V., Every place admits local uniformization in a finite extension of the function field, Adv. Math. 221 (2009), 428-453.
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements resolution of surface singularities; Newton polygon; equimultiple locus; blowup
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements maximum for the dimension of linear series of given degree on a smooth plane curve of degree d C. Ciliberto , Alcune applicazioni di un classico procedimento di Castelnuovo , Sem. di variabili Complesse, Univ. di Bologna, 19...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Beilinson conjectures; motives; Hecke characters of imaginary quadratic fields; regulator map; \(p\)-adic \(K\)-theory; Galois cohomology group; \(p\)-adic \(L\)-series Geisser, p-adic K-theory of Hecke characters of imagina...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements qubits; entanglement; system of parameters; Gorenstein; Cohen-Macaulay DOI: 10.1007/s10440-005-0471-3
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements germs of analytic plane curves; moduli space of germs; Tjurina number; equisingular miniversal deformation Peraire, R.: Moduli of plane curve singularities with a single characteristic exponent, Proc. amer. Math. soc. 126, N...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements semi-abelian analogue of Schanuel's conjecture; linear disjointness; algebraic independence; semi-abelian exponential; generalized semi-abelian logarithm
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements unipotent elements; nilpotent elements; special orthogonal groups; unipotent classes; unipotent pieces; reductive connected algebraic groups; varieties of Borel subgroups G. Lusztig, Unipotent elements in small characteristi...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements exterior power; algebra of minors; orbit structure; singular locus; general linear group Bruns, W.; Conca, A.: The variety of exterior powers of linear maps, J. algebra 322, 2927-2949 (2009)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements general linear groups; Borel subgroups; Lie algebras of matrices; Lie ideals; dense orbits; quasi-hereditary algebras; dimension vectors Goodwin, S.M., Hille, L.: Prehomogeneous spaces for Borel subgroups of general linear g...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements algebraic geometry; syzygies; projective normality; normal presentation; higher dimensional varieties with nef canonical bundle; Fujita's conjecture; pluricanonical linear systems on varieties of general type
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements homological dimension; linear resolutions; Diophantine equations; ternary quadratic forms
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements abelian varieties; Jacobians; automorphisms of curves; abelian functions; soliton equations; integrable Hamiltonian systems; Poincaré reducibility; KP equation; KdV equation; Krichever theory; Calgorero-Moser system Emma Pre...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements modification; survey; tangent hyperplanes; normal surface singularity; Milnor numbers; tangent cone; resolution of normal surface singularities
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements injective homomorphism of product of local rings; length formulas for the local cohomology; module of differential forms on a complete intersection with isolated singularity Bruns, W. andVetter, U., Length formulas for the l...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements polynomial; isolated zero of a system of polynomials; multiplicity
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Brill-Noether theory; moduli space of curves, divisors on the moduli space of curves; linear series; special divisors Choi, Y.; Kim, S.; Kim, Y.: Remarks on brill-Noether divisors and Hilbert schemes, J. pure appl. Algebra 2...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements general linear group; symmetric product; complete reducibility; irreducible representations; space of invariants; symmetric group
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements quasianalytic; Denjoy-Carleman class; resolution of singularities Bierstone E., Milman P.D.: Resolution of singularities in Denjoy-Carleman classes. Selecta Math. (N.S.) 10(1), 1--28 (2004)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements surfaces of general type; rational double points; linear systems; intermediated embeddings; \((-2)\)-curves
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Transformations of abelian functions
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements resolution of singularities; curves; surfaces; threefolds Hauser [Hauser 00] H., Resolution of Singularities (2000)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements resolution of singularities; curve singularities B. Teissier, Introduction to curve singularities, Singularity theory (Trieste, 1991), World Scientific Publishing (1995), 866-893.
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements quadratic forms; pair of forms; asymptotic formula; smooth intersection; Delta-method; Kloosterman refinement; double Kloosterman refinement R. Munshi, Pairs of quadrics in 11 variables, preprint (2013), .
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements System of equations; roots; algebraic funcion; determinant
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements real toric variety; shellability; root system of type B
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements extension of varieties; Veronesean varieties; Segre varieties; not hyperplane sections; quadratic equations; not a complete inersection L'vovski S.M. (1989) On the extension of varieties defined by quadratic equations. Math....
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Green's conjecture; linear series Clifford index; rational ribbon; resolution Clifford index; canonical curve conjecture D. Eisenbud and M. Green, Clifford indices of ribbons, Trans. Amer. Math. Soc. 347 (1995), no. 3, 757--...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements system of congruences; Poincaré series; p-adic units; poles; singularities Jay R. Goldman, Numbers of solutions of congruences: Poincaré series for algebraic curves, Adv. in Math. 62 (1986), no. 1, 68 -- 83.
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements normal excellent equicharacteristic local rings; effective Weil divisor; global functions; Cartier divisor; resolution of singularities
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements supersingular curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; torsion pair; order of point; Legendre symbol; quadratic residue; quadratic nonresidue
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Birch--Swinnerton-Dyer conjecture; rank; group of rational points; elliptic curves; class number; quadratic fields
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements k-gonal curve; double cover of a nonsingular complete curve; linear series Del Centina, A.: \(g{\kappa}1\) on an unramified double cover of a k-gonal curve and applications. Rend. sem. Mat. Torino 41, 53-63 (1983)
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Painlevé equations; birational canonical transformations; Hamiltonian system Okamoto, Kazuo, Studies on the {P}ainlevé equations. {III}. {S}econd and fourth {P}ainlevé equations, {\(P_{{\mathrm II}}\)} and {\(P_{{\mathrm IV}...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements singular quadratic complexes; quintic curves; Cremona transformations
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements apolarity; Gorenstein algebra; sum of powers of linear forms; catalecticant matrices; determinantal loci; punctual Hilbert schemes Anthony Iarrobino and Vassil Kanev. \textit{Power Sums, Gorenstein Algebras, and Determinanta...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements birational transformations; representability of functors; Zariski topology; algebraic groups
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Frobenius map; tight closure; Hochster-Roberts theorem; rings of invariants; Briançon-Skoda theorem; vanishing theorems; adjoint linear series Karen E. Smith, Tight closure and vanishing theorems, School on Vanishing Theorem...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements irreducibility of system of irreducible plane curves; abelian; fundamental group of the complement of a nodal plane curve; degree n Oscar Zariski, On the problem of irreducibility of the algebraic system of irreducible plane...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Fano complete intersection; maximal singularity; mobile linear system; multiplicity
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements \(K3\) surface; Kummer quartic; minimal resolution of singularities; singular plane Naruki I. (1991). On metamorphosis of Kummer surfaces. Hokkaido Math. J. 20(2): 407--415
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements \(SL_ 2\); algebra of invariant polynomials; coregular linear groups
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements spectral space and spectral map; star and semistar operations; Zariski, constructible, inverse and ultrafilter topologies; Gabriel-Popescu localizing system; Riemann-Zariski space of valuation domains; Kronecker function rin...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements counting; equidistribution; rational points; mixing; symmetric spaces; polar decomposition; resolution of singularities Y. Benoist, Effective equidistribution of \(S\)-integral points on symmetric varieties, Ann. Inst. Fouri...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements linear syzygies; graded Betti numbers; partial elimination ideals; inner projection; varieties of small degree Han, K.; Kwak, S.: Sharp bounds for higher linear syzygies and classifications of projective varieties. Math. ann...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements multiplicity; local ring; graded linear series; projective scheme; volume of a line bundle; Kodaira-Iitaka dimension S. D. Cutkosky, ''Multiplicities of graded families of linear series and ideals,'' arXiv: 1301.5613 [math.A...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements neural network of final ring; secret sharing schemes; system of residual classes; elliptic curves
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements generating functions; transitive permutation factorizations; symmetric functions; Jucys-Murphy elements; contents of partitions
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements purely inseparable extension of exponent 1; Brauer group; p-symbols; transformation formulas; differential p-crossed products
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements \(ETH\)-cofinite modules; local cohomology; Serre subcategories; system of ideals
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements algorithm for subsystems of a root system; simple elliptic singularities; singular del Pezzo surfaces; Coxeter diagram; intersections of two quadrics; deformations of singularities C.\ T.\ C. Wall, Root systems, subsystems a...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements deformation spaces of plane curve singularities; equisingular locus; equigeneric locus; equiclassical locus; dimensions of families of plane curves Diaz, S., and Harris, J.: Ideals associated to deformations of singular plan...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements Jacobian variety; rational points; linear pencil of projective plane curves; Mordell-Weil lattices; Manin-Shafarevich theorem; height pairing; Lefschetz pencils of hyperplane sections Shioda, T.: Generalization of a theorem ...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements motives; triangulated categories; cohomology; weight structures; resolution of singularities; alterations Bondarko, M.V., \(\mathbb{Z} [\frac{1}{p}]\)-motivic resolution of singularities, Compos. math., 147, 1434-1446, (2011...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements abelian varieties with complex multiplication; periods of first and second kind; Jacobian of the Fermat curves; linear independence of values of the Beta-function; covering radius Wolfart, J., Der überlagerungsradius gewisse...
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements resolution of singularities; hypersurfaces; Maple Gábor Bodnár and Josef Schicho, Automated resolution of singularities for hypersurfaces, J. Symbolic Comput. 30 (2000), no. 4, 401 -- 428.
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resolution of linear system; quadratic transformations; Plücker formulas; equisingular elements moduli spaces of linear control systems Helmke U (1985) The topology of a moduli space for linear dynamical systems. Comment Math Helvetici 60: 630--655
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