When does depth stabilize early on?
Commutative Algebra
2015-09-08 v4
Abstract
In this paper we study graded ideals I in a polynomial ring S such that the numerical function f(k)=depth(S/I^k) is constant. We show that, if (i) the Rees algebra of I is Cohen-Macaulay, (ii) the cohomological dimension of I is not larger than the projective dimension of S/I and (iii) the K-algebra generated by some generators of I is a direct summand of S, then f(k) is constant. When I is a square-free monomial ideal, the above criterion includes as special cases all the results of a recent paper by Herzog and Vladoiu. In this combinatorial setting there is a chance that the converse of the above fact holds true.
Cite
@article{arxiv.1407.3967,
title = {When does depth stabilize early on?},
author = {Le Dinh Nam and Matteo Varbaro},
journal= {arXiv preprint arXiv:1407.3967},
year = {2015}
}
Comments
The title has been changed and other minor changes have been done. The paper will appear in Journal of Algebra