% Official template for % https://topology.journals.yorku.ca/index.php/tp/about/submissions % Version 2025-04-25 \documentclass[twoside]{amsart} \usepackage{pacchetto} % Author info %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % First author: \author{Ludovica Buelli} \address{Dipartimento di Matematica; Università di Genova; Via Dodecaneso 35, 16146 Genova, Italia} % Current address (if needed): %\curraddr{} \email{ludovica.buelli@edu.unige.it, ludovica.buelli@hotmail.com} % \thanks{The first author was supported in part by NSF Grant \#000000.} % Second author (if needed): %\author{Author Two} %\address{} %\email{} %\thanks{Support information for the second author.} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title[Locally trivial monodromy of moduli spaces]% {Locally trivial monodromy of moduli spaces\\ of sheaves on Abelian surfaces} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \begin{abstract}The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semi-\linebreak[4]stable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is that the locally trivial monodromy group of a singular moduli space of this type is isomorphic to the monodromy group of a smooth moduli space, extending Markman’s and Mongardi's description to the non-primitive case. \end{abstract} \maketitle \vspace{-5ex} \tableofcontents \vspace{-5ex} \section*{Introduction} \input{intro} \section{Preliminaries} \input{sec1} \section{An injective morphism from \texorpdfstring{$\monlt(K_v(S,H))$}{Mon2lt(Kv(S,H))} to \texorpdfstring{$\mon^{2}(K_w(S,H))$}{Mon2(Kw(S,H))}} \input{sec2} \section{A groupoid representation} \input{sec3} \section{The locally trivial monodromy group} \input{sec4} \appendix \section{Some lattice theory results} \input{appendix} \bibliographystyle{alpha} \begin{thebibliography}{Aaaaaaaa} \input{bibliography} \end{thebibliography} %\printbibliography \end{document}