{"title":"超平面排列的希尔伯特霍奇理想系列","authors":"Bradley Dirks, M. Mustaţă","doi":"10.5427/jsing.2020.20j","DOIUrl":null,"url":null,"abstract":"Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheaves on X in terms of the motivic Chern class of the complement of the support of D. As an application, we compute the generating function for the Hilbert series of Hodge ideals of a hyperplane arrangement in terms of the Poincare polynomial of the arrangement.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"07 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Hilbert series of Hodge ideals of hyperplane arrangements\",\"authors\":\"Bradley Dirks, M. Mustaţă\",\"doi\":\"10.5427/jsing.2020.20j\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheaves on X in terms of the motivic Chern class of the complement of the support of D. As an application, we compute the generating function for the Hilbert series of Hodge ideals of a hyperplane arrangement in terms of the Poincare polynomial of the arrangement.\",\"PeriodicalId\":278201,\"journal\":{\"name\":\"arXiv: Algebraic Geometry\",\"volume\":\"07 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5427/jsing.2020.20j\",\"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/10.5427/jsing.2020.20j","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Hilbert series of Hodge ideals of hyperplane arrangements
Given a reduced effective divisor D on a smooth variety X, we describe the generating function for the classes of the Hodge ideals of D in the Grothendieck group of coherent sheaves on X in terms of the motivic Chern class of the complement of the support of D. As an application, we compute the generating function for the Hilbert series of Hodge ideals of a hyperplane arrangement in terms of the Poincare polynomial of the arrangement.