The Regularity of Tor and Graded Betti Numbers
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
Let S=K[x_1,..., x_n], let A,B be finitely generated graded S-modules, and let m=(x_1,...,x_n). We give bounds for the Castelnuovo-Mumford regularity of the local cohomology of Tor_i(A,B) under the assumption that the Krull dimension of Tor_1(A,B) is at most 1. We apply the results to syzygies, Groebner bases, products and powers of ideals, and to the relationship of the Rees and Symmetric algebras. For example we show that any homogeneous linearly presented m-primary ideal has some power equal to a power of m; and if the first (roughly) (n-1)/2 steps of the resolution of I are linear, then I^2 is a power of m.
Keywords
Cite
@article{arxiv.math/0405373,
title = {The Regularity of Tor and Graded Betti Numbers},
author = {David Eisenbud and Craig Huneke and Bernd Ulrich},
journal= {arXiv preprint arXiv:math/0405373},
year = {2007}
}