The leading ideal of a complete intersection of height two, Part II

Let (S,n) be a regular local ring and let I=(f,g) be an ideal in S generated by a regular sequence f,g of length two. Let R=S/I and . As in [S. Goto, W. Heinzer, M.-K. Kim, The leading ideal of a complete intersection of height two, J. Algebra 298 (2006) 238–247], we examine the leading form ideal I* of I in the associated graded ring G=grn(S). If is Cohen–Macaulay, we describe precisely the Hilbert series in terms of the degrees of homogeneous generators of I* and of their successive GCDʹs. If D=GCD(f*,g*) is a prime element of grn(S) that is regular on , we prove that I* is 3-generated and a perfect ideal. If , where h I is such that h* is of minimal degree in I* (f*,g*)grn(S), we prove I* is 3-generated and a perfect ideal of grn(S), so is a Cohen–Macaulay ring. We give several examples to illustrate our theorems.