{"title":"希尔伯特级数的Dedekind和与解析","authors":"Shengtian Zhou","doi":"10.1216/jca.2021.13.281","DOIUrl":null,"url":null,"abstract":"Given a polarized variety (X,D), we can associate a graded ring and a Hilbert series. Assume D is an ample ℚ Cartier divisor, and (X,D) is quasi smooth and projectively Gorenstein, we give a parsing formula for the Hilbert series according to their singularities. Here we allow the variety to have singularities of dimension ≤1, that is, both singularities of dimension 1 and singular points, extending a 2013 result of Buckley, Reid and the author about varieties with only isolated singularities.","PeriodicalId":49037,"journal":{"name":"Journal of Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dedekind sums and parsing of Hilbert series\",\"authors\":\"Shengtian Zhou\",\"doi\":\"10.1216/jca.2021.13.281\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a polarized variety (X,D), we can associate a graded ring and a Hilbert series. Assume D is an ample ℚ Cartier divisor, and (X,D) is quasi smooth and projectively Gorenstein, we give a parsing formula for the Hilbert series according to their singularities. Here we allow the variety to have singularities of dimension ≤1, that is, both singularities of dimension 1 and singular points, extending a 2013 result of Buckley, Reid and the author about varieties with only isolated singularities.\",\"PeriodicalId\":49037,\"journal\":{\"name\":\"Journal of Commutative Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Commutative Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1216/jca.2021.13.281\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Commutative Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jca.2021.13.281","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Given a polarized variety (X,D), we can associate a graded ring and a Hilbert series. Assume D is an ample ℚ Cartier divisor, and (X,D) is quasi smooth and projectively Gorenstein, we give a parsing formula for the Hilbert series according to their singularities. Here we allow the variety to have singularities of dimension ≤1, that is, both singularities of dimension 1 and singular points, extending a 2013 result of Buckley, Reid and the author about varieties with only isolated singularities.
期刊介绍：
Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids.
The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.
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