Ideals with Larger Projective Dimension and Regularity
Commutative Algebra
2011-01-19 v1
Abstract
We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows asymptotically as sqrt{d}^(sqrt(d) - 1).
Cite
@article{arxiv.1101.3368,
title = {Ideals with Larger Projective Dimension and Regularity},
author = {Jesse Beder and Jason McCullough and Luis Nunez-Betancourt and Alexandra Seceleanu and Bart Snapp and Branden Stone},
journal= {arXiv preprint arXiv:1101.3368},
year = {2011}
}
Comments
10 pages. This work was completed at the MRC for Commutative Algebra in Snowbird, UT, which was generously supported by the AMS