超卡勒变上光滑但非交错的剪子模数

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-13 DOI:arxiv-2409.08991

Andreas Krug, Fabian Reede, Ziyu Zhang

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摘要

对于一个无性曲面 $A$，我们考虑了广义库默尔综$K_n(A)$上的稳定向量束，其中$n>1$。我们证明，模空间中包含与阶为 $0$ 的线束相关的同调束的连通部分与双无常曲面在一点上的炸开是同构的。我们认为这是第一个具有非三维典型束的光滑分量的实例。

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

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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arXiv - MATH - Algebraic Geometry

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