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.

arXiv comment18 pages. Final version. Simplified and shortened some proofs after referee report. Comments welcome!

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Cited by in corpus (2)

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