Syzygies in Hilbert schemes of complete intersections

Caviglia, Giulio; Sammartano, Alessio

doi:10.1016/j.jalgebra.2022.12.015

Journal of Algebra

2023

DOI: 10.1016/j.jalgebra.2022.12.015

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Syzygies in Hilbert schemes of complete intersections

Giulio Caviglia¹,

Alessio Sammartano²

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2024

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Bounds for syzygies of monomial curves

Caviglia,

Moscariello,

Sammartano

2024

Proc. Amer. Math. Soc.

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Let Γ ⊆ N \Gamma \subseteq \mathbb {N} be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of Γ \Gamma which depends only on the width of Γ \Gamma , that is, the difference between the largest and the smallest generator of Γ \Gamma . In this way, we make progress towards a conjecture of Herzog and Stamate [J. Algebra 418 (2014), pp. 8–28]. 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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Bounds for syzygies of monomial curves

Caviglia,

Moscariello,

Sammartano

2024

Proc. Amer. Math. Soc.

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Syzygies in Hilbert schemes of complete intersections

Cited by 1 publication

References 27 publications

Bounds for syzygies of monomial curves

Bounds for syzygies of monomial curves

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