{"title":"Variation of stable birational types in positive characteristic","authors":"Stefan Schreieder","doi":"10.46298/epiga.2020.volume3.5728","DOIUrl":null,"url":null,"abstract":"Let k be an uncountable algebraically closed field and let Y be a smooth\nprojective k-variety which does not admit a decomposition of the diagonal. We\nprove that Y is not stably birational to a very general hypersurface of any\ngiven degree and dimension. We use this to study the variation of the stable\nbirational types of Fano hypersurfaces over fields of arbitrary characteristic.\nThis had been initiated by Shinder, whose method works in characteristic zero.\n\n Comment: 14 pages; final version, published in EPIGA","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2020.volume3.5728","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
Let k be an uncountable algebraically closed field and let Y be a smooth
projective k-variety which does not admit a decomposition of the diagonal. We
prove that Y is not stably birational to a very general hypersurface of any
given degree and dimension. We use this to study the variation of the stable
birational types of Fano hypersurfaces over fields of arbitrary characteristic.
This had been initiated by Shinder, whose method works in characteristic zero.
Comment: 14 pages; final version, published in EPIGA
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