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Singularities on normal varieties

Part of: Local theory Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  01 March 2009

Tommaso de Fernex  and
Christopher D. Hacon
Tommaso de Fernex
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 48112-0090, USA (email: [email protected])
Christopher D. Hacon
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 48112-0090, USA (email: [email protected])
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Abstract

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In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being ℚ-Gorenstein or the pair being log ℚ-Gorenstein. The main features of the theory extend to this setting in a natural way.

Keywords

divisorial valuationrelative canonical divisorsingularities of pairsmultiplier ideals

MSC classification

Secondary: 14B05: Singularities 14J17: Singularities 14E15: Global theory and resolution of singularities
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 2 , March 2009 , pp. 393 - 414
Copyright
Copyright © Foundation Compositio Mathematica 2009

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