论K3$^{[n]}$型投影超凯勒积分的交映双理自映射

Pub Date : 2024-05-29 DOI:10.1093/imrn/rnae112

Yajnaseni Dutta, Dominique Mattei, Yulieth Prieto-Montañez

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引用次数: 0

摘要

我们证明，K3$^{[n]}$型的投影超凯勒流形，如果允许有限阶的非难交映双向自映射，则与 K3 曲面上的稳定（扭曲）相干剪切的模空间同构。受这一结果的启发，我们分析了剪切的模空间的动锥上的反射，并确定它们何时来自双向卷积。

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On Symplectic Birational Self-Maps of Projective Hyperkähler Manifolds of K3$^{[n]}$-Type

We prove that projective hyperkähler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution.

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