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arXiv · 2108.05339

Stable vector bundles on generalized Kummer varieties

Fabian Reede·Ziyu Zhang
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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 $n\geqslant 2$. 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 $\widehat{A}$ 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.

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Fabian Reede, Ziyu Zhang. 2022-04-21. Stable vector bundles on generalized Kummer varieties. https://doi.org/10.1515/forum-2021-0249

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