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Castelnuovo-Mumford regularity of simplicial semigroup rings with isolated singularity

Authors:	Jü rgen Herzog Takayuki Hibi

Institution:	FB6 Mathematik und Informatik, Universität -- GHS -- Essen, Postfach 103764, 45117 Essen, Germany ; Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560--0043, Japan

Abstract:	Let $S = Kx_1, \ldots, x_n]$ be the polynomial ring in $n \geq 2$ variables over a field and $\mathfrak{m}$ its graded maximal ideal. Let $f_1,\ldots, f_m \in S$ be homogeneous polynomials of degree $d-1\geq 2$ generating an $\mathfrak{m}$ -primary ideal, and let $g_1,\ldots,g_r\in S$ be arbitrary homogeneous polynomials of degree . In the present paper it will be proved that the Castelnuovo-Mumford regularity of the standard graded -algebra $A=K\{f_ix_j\}_{\substack{i=1,\ldots,m j=1,\ldots,n}}, g_1,\ldots, g_r]$ is at most . By virtue of this result, it follows that the regularity of a simplicial semigroup ring with isolated singularity is at most $e(KC]) - \operatorname{codim}(KC])$ , where is the multiplicity of and $\operatorname{codim}(KC])$ is the codimension of .

Keywords:	Castelnuovo--Mumford regularity Eisenbud--Goto conjecture simplicial semigroup ring isolated singularity

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