{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:37Z","timestamp":1753893817605,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $H$ be an $n$-generated numerical semigroup such that its tangent cone\u00a0$\\operatorname{gr}_\\mathfrak{m} K[H]$ is defined by quadratic relations. We\u00a0show that if $n&lt;5$ then $\\operatorname{gr}_\\mathfrak{m} K[H]$ is Cohen-Macaulay, and for $n=5$ we explicitly describe the semigroups $H$ such\u00a0that $\\operatorname{gr}_\\mathfrak{m} K[H]$ is not Cohen-Macaulay. As an\u00a0application we show that if the field $K$ is algebraically closed and of\u00a0characteristic different from two, and $n\\leq 5$ then\u00a0$\\operatorname{gr}_\\mathfrak{m} K[H]$ is Koszul if and only if (possibly after\u00a0a change of coordinates) its defining ideal has a quadratic Gr\u00f6bner basis.<\/jats:p>","DOI":"10.37236\/5793","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:36:59Z","timestamp":1578688619000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Cohen-Macaulay Property for Quadratic Tangent Cones"],"prefix":"10.37236","volume":"23","author":[{"given":"Dumitru I.","family":"Stamate","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,8,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:17:40Z","timestamp":1579238260000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,5]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5793","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,8,5]]},"article-number":"P3.20"}}