{"title":"仿射空间商上的环面作用","authors":"Ana-Maria Brecan, H. Franzen","doi":"10.46298/epiga.2023.10073","DOIUrl":null,"url":null,"abstract":"We study the locus of fixed points of a torus action on a GIT quotient of a\ncomplex vector space by a reductive complex algebraic group which acts\nlinearly. We show that, under the assumption that $G$ acts freely on the stable\nlocus, the components of the fixed point locus are again GIT quotients of\nlinear subspaces by Levi subgroups.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Torus Actions on Quotients of Affine Spaces\",\"authors\":\"Ana-Maria Brecan, H. Franzen\",\"doi\":\"10.46298/epiga.2023.10073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the locus of fixed points of a torus action on a GIT quotient of a\\ncomplex vector space by a reductive complex algebraic group which acts\\nlinearly. We show that, under the assumption that $G$ acts freely on the stable\\nlocus, the components of the fixed point locus are again GIT quotients of\\nlinear subspaces by Levi subgroups.\",\"PeriodicalId\":41470,\"journal\":{\"name\":\"Epijournal de Geometrie Algebrique\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Epijournal de Geometrie Algebrique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/epiga.2023.10073\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epijournal de Geometrie Algebrique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2023.10073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study the locus of fixed points of a torus action on a GIT quotient of a
complex vector space by a reductive complex algebraic group which acts
linearly. We show that, under the assumption that $G$ acts freely on the stable
locus, the components of the fixed point locus are again GIT quotients of
linear subspaces by Levi subgroups.
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