, Volume 98, Issue 3, pp 377-390

Blow-up rings and rational singularities

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Abstract:

Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let IA 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