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On the lengths of Koszul homology modules and generalized fractions

Published online by Cambridge University Press:  24 October 2008

N. T. Cuong  and
N. D. Minh
N. T. Cuong
Affiliation:
Hanoi Institute of Mathematics, P.O. Box 631, Bo Ho, 10.000 Hanoi, Vietnam
N. D. Minh
Affiliation:
Hanoi Institute of Mathematics, P.O. Box 631, Bo Ho, 10.000 Hanoi, Vietnam
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Extract

Throughout this paper, let A be a Noetherian local ring with maximal ideal m and M a finitely generated A-module with d = dimAM ≥ 1. Denote by N the set of all positive integers.

Let x = (x1, …, xd) be a system of parameters (s.o.p) for M and let

We consider the following two problems: (i) When is the length of Koszul homology

a polynomial in n for all k = 0, …, d and n1; …, nd sufficiently large (n ≫ 0)?

(ii) Is the length of the generalized fraction in a polynomial in n for n ≫ 0?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 31 - 42
Copyright
Copyright © Cambridge Philosophical Society 1996

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