{"title":"单项式方案的分离类","authors":"P. Aluffi","doi":"10.3934/era.2013.20.55","DOIUrl":null,"url":null,"abstract":"We propose an explicit formula for the Segre classes of monomial \nsubschemes of nonsingular varieties, such as schemes defined by \nmonomial ideals in projective space. The Segre class is expressed as \na formal integral on a region bounded by the corresponding Newton \npolyhedron. We prove this formula for monomial ideals in two variables \nand verify it for some families of examples in any number of \nvariables.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"20 1","pages":"55-70"},"PeriodicalIF":0.0000,"publicationDate":"2013-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Segre classes of monomial schemes\",\"authors\":\"P. Aluffi\",\"doi\":\"10.3934/era.2013.20.55\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose an explicit formula for the Segre classes of monomial \\nsubschemes of nonsingular varieties, such as schemes defined by \\nmonomial ideals in projective space. The Segre class is expressed as \\na formal integral on a region bounded by the corresponding Newton \\npolyhedron. We prove this formula for monomial ideals in two variables \\nand verify it for some families of examples in any number of \\nvariables.\",\"PeriodicalId\":53151,\"journal\":{\"name\":\"Electronic Research Announcements in Mathematical Sciences\",\"volume\":\"20 1\",\"pages\":\"55-70\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Research Announcements in Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/era.2013.20.55\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/era.2013.20.55","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
We propose an explicit formula for the Segre classes of monomial
subschemes of nonsingular varieties, such as schemes defined by
monomial ideals in projective space. The Segre class is expressed as
a formal integral on a region bounded by the corresponding Newton
polyhedron. We prove this formula for monomial ideals in two variables
and verify it for some families of examples in any number of
variables.
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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