{"title":"On the multiplicity of tangent cones of monomial curves","authors":"Alessio Sammartano","doi":"10.4310/ARKIV.2019.v57.n1.a11","DOIUrl":null,"url":null,"abstract":"Let S be a numerical semigroup, R the local ring of the monomial curve singularity associated to S, and G its associated graded ring. In this paper we provide a sharp upper bound for the least positive integer in S in terms of the codimension and the maximum degree of the equations of G, when G is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ARKIV.2019.v57.n1.a11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Let S be a numerical semigroup, R the local ring of the monomial curve singularity associated to S, and G its associated graded ring. In this paper we provide a sharp upper bound for the least positive integer in S in terms of the codimension and the maximum degree of the equations of G, when G is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.
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