A smooth but non-symplectic moduli of sheaves on a hyperkähler variety

Andreas Krug; Fabian Reede; Ziyu Zhang

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arXiv · 2409.08991

A smooth but non-symplectic moduli of sheaves on a hyperkähler variety

Andreas Krug·Fabian Reede·Ziyu Zhang

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Abstract

For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles of degree $0$ is isomorphic to the blowup of the dual abelian surface in one point. We believe that this is the first explicit example of a component which is smooth with a non-trivial canonical bundle.

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BibTeX RIS

Andreas Krug, Fabian Reede, Ziyu Zhang. 2024-09-13. A smooth but non-symplectic moduli of sheaves on a hyperkähler variety. https://arxiv.org/abs/2409.08991

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