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.
On the transcendental lattices of Hyper-Kähler manifolds / B. Piroddi, Á.D. Ríos Ortiz. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 229:1(2025 Jan), pp. 107805.1-107805.22. [10.1016/j.jpaa.2024.107805]
On the transcendental lattices of Hyper-Kähler manifolds
B. Piroddi
Primo
;
2025
Abstract
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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