Blow-up rings and rational singularities

Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let I⊂A be an ideal such that the Rees algebra R _A (I) is Cohen–Macaulay and normal. In this paper we address the question: “When does R _A (I) have rational singularities?” In particular, we study the connection between rational singularities of R _A (I) and the adjoint ideals of the powers I ⁿ (n∋ℕ). Received: 25 May 1998 / Revised version: 20 August 1998