{"title":"一些自同构群是线性代数的","authors":"M. Brion","doi":"10.17323/1609-4514-2021-21-3-453-466","DOIUrl":null,"url":null,"abstract":"Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Automorphism Groups are Linear Algebraic\",\"authors\":\"M. Brion\",\"doi\":\"10.17323/1609-4514-2021-21-3-453-466\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.\",\"PeriodicalId\":278201,\"journal\":{\"name\":\"arXiv: Algebraic Geometry\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17323/1609-4514-2021-21-3-453-466\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17323/1609-4514-2021-21-3-453-466","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.
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