{"title":"The maximal unipotent finite quotient, unusual torsion in Fano\n threefolds, and exceptional Enriques surfaces","authors":"Andrea Fanelli, Stefan Schroer","doi":"10.46298/epiga.2020.volume4.6151","DOIUrl":null,"url":null,"abstract":"We introduce and study the maximal unipotent finite quotient for algebraic\ngroup schemes in positive characteristics. Applied to Picard schemes, this\nquotient encodes unusual torsion. We construct integral Fano threefolds where\nsuch unusual torsion actually appears. The existence of such threefolds is\nsurprising, because the torsion vanishes for del Pezzo surfaces. Our\nconstruction relies on the theory of exceptional Enriques surfaces, as\ndeveloped by Ekedahl and Shepherd-Barron.\n\n Comment: 29 pages; minor changes","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2020.volume4.6151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We introduce and study the maximal unipotent finite quotient for algebraic
group schemes in positive characteristics. Applied to Picard schemes, this
quotient encodes unusual torsion. We construct integral Fano threefolds where
such unusual torsion actually appears. The existence of such threefolds is
surprising, because the torsion vanishes for del Pezzo surfaces. Our
construction relies on the theory of exceptional Enriques surfaces, as
developed by Ekedahl and Shepherd-Barron.
Comment: 29 pages; minor changes
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