Bounds for syzygies of monomial curves
Commutative Algebra
2024-08-05 v2 Combinatorics
Abstract
Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the difference between the largest and the smallest generator of G. In this way, we make progress towards a conjecture of Herzog and Stamate. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width.
Keywords
Cite
@article{arxiv.2307.05770,
title = {Bounds for syzygies of monomial curves},
author = {Giulio Caviglia and Alessio Moscariello and Alessio Sammartano},
journal= {arXiv preprint arXiv:2307.05770},
year = {2024}
}
Comments
Fixed typos. Final version, to appear on Proc. Amer. Math. Soc