COHEN-MACAULAY LOCAL-RINGS OF DIMENSION-2 AND AN EXTENDED VERSION OF A CONJECTURE OF SALLY,J

In this paper we prove an extended version of a conjecture of J. Sally . Let (A,M) be a Cohen-Macaulay local ring of dimension d, multiplicit y e and embedding codimension h. If the initial degree of A is bigger than or equal to t and e = (h+t-1/h) + 1, we prove that the depth of t he associated graded ring of A is at least d - 1 and the h-vector of A has no negative components. The conjecture of Sally was dealing with the case t = 2 and was proved by these authors in a previous paper. So me new formulas relating certain numerical characters of a two-dimensi onal Cohen-Macaulay local ring are also given. (C) 1997 Published by E lsevier Science B.V.