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

Authors:
M. Brodmann and F. Rohrer

Journal:
Proc. Amer. Math. Soc. **133** (2005), 987-993

MSC (2000):
Primary 13D45, 13E10

Published electronically:
November 19, 2004

MathSciNet review:
2117198

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Noetherian homogeneous 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 . We show that the first Hilbert-Samuel coefficient of the -th graded component of with respect to is antipolynomial of degree in . In addition, we prove that the postulation numbers of the components with respect to have a common upper bound.

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Additional Information

**M. Brodmann**

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

Email:
brodmann@math.unizh.ch

**F. Rohrer**

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

Email:
fred@math.unizh.ch

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07779-2

Keywords:
Local cohomology modules,
graded components,
Hilbert-Samuel polynomials

Received by editor(s):
December 1, 2003

Published electronically:
November 19, 2004

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2004
American Mathematical Society