Benjamin Bakker, Thomas W. Grimm, C. Schnell, Jacob Tsimerman
{"title":"Finiteness for self-dual classes in integral variations of Hodge structure","authors":"Benjamin Bakker, Thomas W. Grimm, C. Schnell, Jacob Tsimerman","doi":"10.46298/epiga.2023.specialvolumeinhonourofclairevoisin.9626","DOIUrl":null,"url":null,"abstract":"We generalize the finiteness theorem for the locus of Hodge classes with\nfixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge\nclasses to self-dual classes. The proof uses the definability of period\nmappings in the o-minimal structure $\\mathbb{R}_{\\mathrm{an},\\exp}$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2023.specialvolumeinhonourofclairevoisin.9626","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
We generalize the finiteness theorem for the locus of Hodge classes with
fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge
classes to self-dual classes. The proof uses the definability of period
mappings in the o-minimal structure $\mathbb{R}_{\mathrm{an},\exp}$.