{"title":"Grassmannian Richardson变种的光滑环面商","authors":"Sarjick Bakshi","doi":"10.1142/s0219498825501245","DOIUrl":null,"url":null,"abstract":"Let $k$ and $n$ be positive coprime integers with $k<n$. Let $T$ denote the subgroup of diagonal matrices in $SL(n,\\mathbb{C})$. We study the GIT quotient of Richardson varieties $X^v_w$ in the Grassmannian $\\mathrm{Gr}_{k,n}$ by $T$ with respect to a $T$-linearised line bundle $\\cal{L}$ corresponding to the Pl\\\"{u}cker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety $T \\backslash\\mkern-6mu\\backslash (X_w^v)^{ss}_T({\\cal L})$ to be smooth.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Smooth torus quotients of Richardson varieties in the Grassmannian\",\"authors\":\"Sarjick Bakshi\",\"doi\":\"10.1142/s0219498825501245\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $k$ and $n$ be positive coprime integers with $k<n$. Let $T$ denote the subgroup of diagonal matrices in $SL(n,\\\\mathbb{C})$. We study the GIT quotient of Richardson varieties $X^v_w$ in the Grassmannian $\\\\mathrm{Gr}_{k,n}$ by $T$ with respect to a $T$-linearised line bundle $\\\\cal{L}$ corresponding to the Pl\\\\\\\"{u}cker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety $T \\\\backslash\\\\mkern-6mu\\\\backslash (X_w^v)^{ss}_T({\\\\cal L})$ to be smooth.\",\"PeriodicalId\":54888,\"journal\":{\"name\":\"Journal of Algebra and Its Applications\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219498825501245\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219498825501245","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
期刊介绍:
The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.