On the transcendental lattices of Hyper-Kähler manifolds

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 l...

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Bibliographic Details
Published in:Journal of pure and applied algebra Vol. 229; no. 1; p. 107805
Main Authors: Piroddi, Benedetta, Ríos Ortiz, Ángel David
Format: Journal Article
Language:English
Published: Elsevier B.V 01-01-2025
Subjects:
14J42
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Summary: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.
ISSN:0022-4049
DOI:10.1016/j.jpaa.2024.107805