{"title":"关于单曲线切锥的多重性","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":55569,"journal":{"name":"Arkiv for Matematik","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2017-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":55569,\"journal\":{\"name\":\"Arkiv for Matematik\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2017-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arkiv for Matematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ARKIV.2019.v57.n1.a11\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv for Matematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ARKIV.2019.v57.n1.a11","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the multiplicity of tangent cones of monomial curves
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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