Complete Intersection Monomial Curves and the Cohen—Macaulayness of Their Tangent Cones

Abstract

Let C(n) be a complete intersection monomial curve in the 4dimensional affine space. In this paper we study the complete intersection property of the monomial curve C(n + wv), where w > 0 is an integer and v ∈ N 4 . Also we investigate the Cohen-Macaulayness of the tangent cone of C(n + wv).

Hilbert series of tangent cones for Gorenstein monomial curves in A4(K)

“…Recently, there has been an increased interest in studying the behaviour of the Betti numbers of a shifted toric ideal I(a + mu), where m ≥ 0 is an integer and u ∈ N n , see [3], [4], [7], [8], [13]. That's mainly due to a conjecture of J. Herzog and H. Srinivasan saying that the Betti numbers of I(a 1 + m, .…”