The Koszulness of numerical semigroup rings of minimal multiplicity

Abstract

 Let  be a numerical semigroup ring over a field k and  is the associated graded ring of .  In this paper, we show that  is a Cohen-Macaulay ring, provided H has minimal multiplicity. As a consequence, we conclude that the numerical semigroup ring  of minimal multiplicity is a Koszul ring, i.e., the residue field k has a linear free resolution.