Ugo Bruzzo, Rodrigo Gondim, Rafael Holanda, William D. Montoya
{"title":"Cox-Gorenstein algebras","authors":"Ugo Bruzzo, Rodrigo Gondim, Rafael Holanda, William D. Montoya","doi":"arxiv-2407.17811","DOIUrl":null,"url":null,"abstract":"This paper is a first step in the study of nonstandard graded algebras having\nPoincar\\'e duality and their Lefschetz properties. We prove the equivalence\nbetween the toric setup and the G-graded one, generalize Macaulay-Matlis\nduality, introduce Lefschetz properties and prove a Hessian criteria in the\nG-graded setup. We prove a special case of the Codimension One Conjecture of\nCattani-Cox-Dickenstein.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.17811","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is a first step in the study of nonstandard graded algebras having
Poincar\'e duality and their Lefschetz properties. We prove the equivalence
between the toric setup and the G-graded one, generalize Macaulay-Matlis
duality, introduce Lefschetz properties and prove a Hessian criteria in the
G-graded setup. We prove a special case of the Codimension One Conjecture of
Cattani-Cox-Dickenstein.
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