Quadratic numerical semigroups and the Koszul property

摘要

Let H be a numerical semigroup. We give effective bounds for the multiplicity e(H) when the associated graded ring gr(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 pseudosymmetric 4-semigroups) we classify those which are Koszul.