{"title":"仿射超平面排列与Jordan类","authors":"G. Carnovale, F. Esposito","doi":"10.4171/jca/48","DOIUrl":null,"url":null,"abstract":"We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.","PeriodicalId":48483,"journal":{"name":"Journal of Combinatorial Algebra","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2018-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Affine hyperplane arrangements and Jordan classes\",\"authors\":\"G. Carnovale, F. Esposito\",\"doi\":\"10.4171/jca/48\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.\",\"PeriodicalId\":48483,\"journal\":{\"name\":\"Journal of Combinatorial Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jca/48\",\"RegionNum\":2,\"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 Combinatorial Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jca/48","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.
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