{"title":"The variety of polar simplices II","authors":"Jelisiejew, Joachim, Ranestad, Kristian, Schreyer, Frank-Olaf","doi":"10.48550/arxiv.2304.00533","DOIUrl":null,"url":null,"abstract":"We discuss the space $VPS(Q,H)$ of ideals with Hilbert function $H=(1,n,n, \\ldots )$ that are apolar to a full rank quadric $Q$. We prove that its components of saturated ideals are closely related to the locus of Gorenstein algebras and to the Slip component in border apolarity. We also point out an important error in~\\cite{RS} and provide the necessary corrections.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv (Cornell University)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arxiv.2304.00533","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
We discuss the space $VPS(Q,H)$ of ideals with Hilbert function $H=(1,n,n, \ldots )$ that are apolar to a full rank quadric $Q$. We prove that its components of saturated ideals are closely related to the locus of Gorenstein algebras and to the Slip component in border apolarity. We also point out an important error in~\cite{RS} and provide the necessary corrections.
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