manuscripta mathematica

, Volume 98, Issue 3, pp 377-390

First online:

Blow-up rings and rational singularities

  • Eero HyryAffiliated withNational Defence College, Santahamina, FIN-00860 Helsinki, Finland.¶e-mail: Eero.Hyry@Helsinki.FI

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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).

Mathematics Subject Classification (1991):Primary: 13A30; Secondary: 14B05, 14F17