REES-ALGEBRAS OF IDEALS HAVING SMALL ANALYTIC DEVIATION

In this article we identify two large families of ideals of a Cohen-Ma caulay (sometimes Gorenstein) local ring whose Rees algebras are Cohen -Macaulay. Our main results imply, for example, that if (R, M) is a re gular local ring and P is a prime ideal of R such that P(n) is unmixed for all n greater-than-or-equal-to 1 , then the Rees algebra R[Pt] is Cohen-Macaulay if either dim(R/P) = 2, or dim(R/P) = 3, R/P is Cohen- Macaulay, and R/P is integrally closed.