Lower Bounds for Betti Numbers of Monomial Ideals
Commutative Algebra
2017-06-30 v1
Abstract
Let I be a monomial ideal of height c in a polynomial ring S over a field k. If I is not generated by a regular sequence, then we show that the sum of the betti numbers of S/I is at least 2^c + 2^{c-1} and characterize when equality holds. Lower bounds for the individual betti numbers are given as well.
Cite
@article{arxiv.1706.09866,
title = {Lower Bounds for Betti Numbers of Monomial Ideals},
author = {Adam Boocher and James Seiner},
journal= {arXiv preprint arXiv:1706.09866},
year = {2017}
}
Comments
11 pages