Minimal free resolution of the associated graded ring of monomial curves of generalized arithmetic sequences

Let A(C)A(C) be the coordinate ring of a monomial curve C⊆AnC⊆An corresponding to the numerical semigroup SS minimally generated by a sequence a0,…,ana0,…,an. In the literature, little is known about the Betti numbers of the corresponding associated graded ring grm(A)grm(A) with respect to the maximal ideal mm of A=A(C)A=A(C). In this paper we characterize the numerical invariants of a minimal free resolution of grm(A)grm(A) in the case a0,…,ana0,…,an is a generalized arithmetic sequence.