On the transcendental lattices of Hyperkähler manifolds

2023/08/24 by Piroddi, Benedetta, Ortiz, Ángel David Ríos
#14J42 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.12869

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, 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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