Let be a numerical semigroup. We give effective bounds for the multiplicity when the associated graded ring 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, -semigroups, symmetric or pseudosymmetric -semigroups) we classify those which are Koszul.
"Quadratic numerical semigroups and the Koszul property." Kyoto J. Math. 57 (3) 585 - 612, September 2017. https://doi.org/10.1215/21562261-2017-0007