Betti numbers of Z^n-graded modules
Commutative Algebra
2007-05-23 v2
Abstract
Let S=K[X_1,...,X_n] be the polynomial ring over a field K. For bounded below Z^n-graded S-modules M and N we show that if Tor^S_p(M,N) is nonzero, then for every i between 0 and p, the dimension of the K-vector space Tor^S_i(M,N) is at least as big as the binomial coefficient (p,i). In particular, we get lower bounds for the total Betti numbers. These results are related to a conjecture of Buchsbaum and Eisenbud.
Cite
@article{arxiv.math/0303349,
title = {Betti numbers of Z^n-graded modules},
author = {Morten Brun and Tim Roemer},
journal= {arXiv preprint arXiv:math/0303349},
year = {2007}
}
Comments
minor modifications