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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21680

# Brodmann, M; Rohrer, F (2005). Hilbert-Samuel coefficients and postulation numbers of graded components of certain local cohomology modules. Proceedings of the American Mathematical Society, 133(4):987-993 (electronic).

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## Abstract

Let be a positively graded commutative Noetherian ring with one-dimensional local base ring . Let be an -primary ideal. Let be a finitely generated graded -module and let . Let denote the -th local cohomology module of with respect to the irrelevant ideal of . The main results in this paper are: "(a)" Assume that for all . Then there is a polynomial of degree such that for all , e_1(_0,H^i_(M)_n)=S(n), where is the so-called first Hilbert-Samuel coefficient of with respect to . "(b)" There is some such that for all , where is the postulation number of the -module with respect to .

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Local cohomology modules, graded components, Hilbert-Samuel polynomials English 2005 03 Feb 2010 08:42 09 Jan 2014 09:59 American Mathematical Society 0002-9939 First published in [Proc. Amer. Math. Soc. 133 (2005), no. 4, 987--993 (electronic)], published by the American Mathematical Society 10.1090/S0002-9939-04-07779-2 http://www.ams.org/mathscinet-getitem?mr=2117198 Web of Science®. Times Cited: 1Google Scholar™Scopus®. Citation Count: 1