Bounds for syzygies of monomial curves

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.

Fixed typos. Final version, to appear on Proc. Amer. Math. Soc

Cited by in corpus (2)

• Open problems on relations of numerical semigroups
• On minimal presentations of numerical monoids