Hilbert-Samuel coefficients and postulation numbers of graded components of certain local cohomology modules期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Hilbert-Samuel coefficients and postulation numbers of graded components of certain local cohomology modules

Authors:	M Brodmann F Rohrer

Institution:	Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ; Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Abstract:	Let $R = \bigoplus _{n \geq 0} R_n$ be a Noetherian homogeneous ring with one-dimensional local base ring $(R_0, {\mathfrak m}_0)$ . Let ${\mathfrak q}_0 \subseteq R_0$ be an ${\mathfrak m}_0$ -primary ideal, let be a finitely generated graded -module and let $i \in {\mathbb N}_0$ . Let $H^i_{R_+}(M)$ denote the -th local cohomology module of with respect to the irrelevant ideal $R_+:= \bigoplus _{n > 0} R_n$ of . We show that the first Hilbert-Samuel coefficient $e_1 \big( {\mathfrak q}_0, H^i_{R_+}(M)_n \big)$ of the -th graded component of $H^i_{R_+}(M)$ with respect to ${\mathfrak q}_0$ is antipolynomial of degree in . In addition, we prove that the postulation numbers of the components $H^i_{R_+} (M)_n$ with respect to ${\mathfrak q}_0$ have a common upper bound.

Keywords:	Local cohomology modules graded components Hilbert-Samuel polynomials

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