Work

On the transcendental lattices of Hyper-Kähler manifolds

Year: 2024

Type: article

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.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2024.107805

Authors: Benedetta Piroddi, Ángel David Ríos Ortiz

Institution: University of Milan

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,330

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, H2020 European Research Council