Tautological Sheaves: Stability, Moduli Spaces and Restrictions to Generalised Kummer Varieties

TL;DR

This paper extends stability results of tautological sheaves to higher dimensions and abelian surfaces, exploring their moduli, restrictions to generalized Kummer varieties, and deformation properties, enriching the understanding of stable sheaves on symplectic manifolds.

Contribution

It introduces new stability results for tautological sheaves in higher dimensions and on generalized Kummer varieties, expanding the class of known stable sheaves on symplectic manifolds.

Findings

Extended stability results to higher dimensions and abelian surfaces

Constructed new examples of stable sheaves on irreducible symplectic manifolds

Studied deformation aspects of tautological sheaves

Abstract

Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a big class of new examples of stable sheaves on higher dimensional irreducible symplectic manifolds. Some aspects of deformations of tautological sheaves are studied.