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arXiv · 2307.05770

Bounds for syzygies of monomial curves

Giulio Caviglia·Alessio Moscariello·Alessio Sammartano
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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.

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Giulio Caviglia, Alessio Moscariello, Alessio Sammartano. 2023-07-11. Bounds for syzygies of monomial curves. https://doi.org/10.1090/proc/16862

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