On the Hilbert function of certain rings of monomial curves Original Research Article

Let A = k[tn1, …, tnd] be the coordinate ring of a monomial affine curve C. Under the assumption “n1, …, nd are an arithmetic sequence”, we determine the Hubert function of the associated graded ring grM(A), where M = (tn1, …, tnd)A, and of the coordinate ring A′ of the projective closure of C; further, we prove that grM(A) and A′ are “level”.