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arXiv · 2308.12869

On the transcendental lattices of Hyperk\"ahler manifolds

Benedetta Piroddi·Ángel David Ríos Ortiz
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Abstract

We introduce the notion of a Hyper-K\"{a}hler manifold $X$ induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian surface, 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-K\"{a}hler manifolds of O'Grady type.

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Benedetta Piroddi, Ángel David Ríos Ortiz. 2023-08-24. On the transcendental lattices of Hyperk\"ahler manifolds. https://arxiv.org/abs/2308.12869

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