Stable vector bundles on generalized Kummer varieties

Abstract

For an abelian surface $A$, we explicitly construct two new families of stable vector bundles on the generalized Kummer variety $K_n(A)$ for $n⩾2$. The first is the family of tautological bundles associated to stable bundles on $A$, and the second is the family of the "wrong-way" fibers of a universal family of stable bundles on the dual abelian surface $\hat{A}$ parametrized by $K_n(A)$. Each family exhibits a smooth connected component in the moduli space of stable bundles on $K_n(A)$, which is holomorphic symplectic but not simply connected, contrary to the case of K3 surfaces.

18 pages. Final version. Simplified and shortened some proofs after referee report. Comments welcome!

References in corpus (3)

• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• Stable vector bundles on a hyper-Kahler manifold with a rank 1 obstruction map are modular
• Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

Cited by in corpus (2)

• Descent of tautological sheaves from Hilbert schemes to Enriques manifolds
• Stability and certain ${\mathbb{P}}^n$-functors