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- W2962746744 abstract "Let $H$ be an $n$-generated numerical semigroup such that its tangent cone $operatorname{gr}_mathfrak{m} K[H]$ is defined by quadratic relations. We show that if $n<5$ then $operatorname{gr}_mathfrak{m} K[H]$ is Cohen-Macaulay, and for $n=5$ we explicitly describe the semigroups $H$ such that $operatorname{gr}_mathfrak{m} K[H]$ is not Cohen-Macaulay. As an application we show that if the field $K$ is algebraically closed and of characteristic different from two, and $nleq 5$ then $operatorname{gr}_mathfrak{m} K[H]$ is Koszul if and only if (possibly after a change of coordinates) its defining ideal has a quadratic Gröbner basis." @default.
- W2962746744 created "2019-07-30" @default.
- W2962746744 creator A5078992205 @default.
- W2962746744 date "2016-08-05" @default.
- W2962746744 modified "2023-09-27" @default.
- W2962746744 title "On the Cohen-Macaulay Property for Quadratic Tangent Cones" @default.
- W2962746744 doi "https://doi.org/10.37236/5793" @default.
- W2962746744 hasPublicationYear "2016" @default.
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