Quadratic numerical semigroups and the Koszul property

Abstract

Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e(H)$ when the associated graded ring ${\mathrm{gr}}_{\mathfrak{m}}K[H]$ is defined by quadrics. We classify Koszul complete intersection semigroups in terms of gluings. Furthermore, for several classes of numerical semigroups considered in the literature (arithmetic, compound, special almost complete intersections, $3$-semigroups, symmetric or pseudo-symmetric $4$-semigroups) we classify those which are Koszul.

24 pages, v3: bibliography updated and minor edits. v2: minor editing changes, added Remark 1.14 and reference to previous work of Rossi and Valla. To appear in the Kyoto Journal of Mathematics

References in corpus (2)

• Numerical semigroups on compound sequences
• Binomial edge ideals and rational normal scrolls

Cited by in corpus (2)

• Betti numbers for numerical semigroup rings
• On the multiplicity of tangent cones of monomial curves