Free resolutions over short Gorenstein local rings
Commutative Algebra
2014-02-26 v2
Abstract
Let R be a local ring with maximal ideal m admitting a non-zero element a\in\fm for which the ideal (0:a) is isomorphic to R/aR. We study minimal free resolutions of finitely generated R-modules M, with particular attention to the case when m^4=0. Let e denote the minimal number of generators of m. If R is Gorenstein with m^4=0 and e\ge 3, we show that \Poi MRt is rational with denominator \HH R{-t} =1-et+et^2-t^3, for each finitely generated R-module M. In particular, this conclusion applies to generic Gorenstein algebras of socle degree 3.
Cite
@article{arxiv.0904.3510,
title = {Free resolutions over short Gorenstein local rings},
author = {Inês B. Henriques and Liana M. Şega},
journal= {arXiv preprint arXiv:0904.3510},
year = {2014}
}
Comments
19 pages; new title, minor changes and extended bibliography