{"title":"On the transcendental lattices of Hyper-Kähler manifolds","authors":"Benedetta Piroddi , Ángel David Ríos Ortiz","doi":"10.1016/j.jpaa.2024.107805","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the notion of a Hyper-Kähler manifold <em>X</em> 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.</p></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924002020/pdfft?md5=edd17e74a859b78f7d2ca46a3aecaa1f&pid=1-s2.0-S0022404924002020-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924002020","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.