论超凯勒流形的超越网格

Pub Date : 2024-09-12 DOI:10.1016/j.jpaa.2024.107805

Benedetta Piroddi , Ángel David Ríos Ortiz

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引用次数: 0

摘要

我们引入了由 K3 型霍奇结构诱导的超凯勒流形 X 的概念。我们针对已知的超凯勒流形的变形类型探讨了这一概念，研究了那些由 K3 或无性曲面（即由其超越晶格的霍奇结构诱导）诱导的超凯勒流形，给出了晶格理论判定它们是否与所述曲面上的剪切的模空间具有双向性的标准。我们着重强调了在奥格雷迪型超凯勒流形这一特殊类别中发现的不同行为。

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On the transcendental lattices of Hyper-Kähler manifolds

We introduce the notion of a Hyper-Kähler manifold X induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of Hyper-Kähler manifolds studying those that are induced by a K3 or abelian surface (that is, induced by the Hodge structure of their transcendental lattice), giving lattice-theoretic criteria to decide whether or not they are birational to a moduli space of sheaves over said surface. We highlight the different behaviors we find for the particular class of Hyper-Kähler manifolds of O'Grady type.

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