Quadratic numerical semigroups and the Koszul property

Abstract

Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e\left(H\right)$ when the associated graded ring ${gr}_{\mathfrak{m}}K\left[H\right]$ 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 pseudosymmetric $4$-semigroups) we classify those which are Koszul.