The leading ideal of a complete intersection of height two

Let (S,n) be a Noetherian local ring and let I=(f,g) be an ideal in S generated by a regular sequence f,g of length two. Assume that the associated graded ring grn(S) of S with respect to n is a UFD. We examine generators of the leading form ideal I∗ of I in grn(S) and prove that I∗ is a perfect ideal of grn(S), if I∗ is 3-generated. Thus, in this case, letting R=S/I and m=n/I, if grn(S) is Cohen–Macaulay, then grm(R)=grn(S)/I∗ is Cohen–Macaulay. As an application, we prove that if (R,m) is a one-dimensional Gorenstein local ring of embedding dimension 3, then grm(R) is Cohen–Macaulay if the reduction number of m is at most 4.