{"title":"On the connectedness of the automorphism group of an affine toric variety","authors":"Veronika Kikteva","doi":"arxiv-2409.10349","DOIUrl":null,"url":null,"abstract":"We obtain a criterion for the automorphism group of an affine toric variety\nto be connected in combinatorial terms and in terms of the divisor class group\nof the variety. The component group of the automorphism group of a\nnon-degenerate affine toric variety is described. In particular, we show that\nthe number of connected components of the automorphism group is finite.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10349","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain a criterion for the automorphism group of an affine toric variety
to be connected in combinatorial terms and in terms of the divisor class group
of the variety. The component group of the automorphism group of a
non-degenerate affine toric variety is described. In particular, we show that
the number of connected components of the automorphism group is finite.
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