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Existence of valuations with smallest normalized volume

Part of: Local theory Topological fields

Published online by Cambridge University Press:  08 March 2018

Harold Blum
Harold Blum*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA email [email protected]://www-personal.umich.edu/∼blum/
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Abstract

Li introduced the normalized volume of a valuation due to its relation to K-semistability. He conjectured that over a Kawamata log terminal (klt) singularity there exists a valuation with smallest normalized volume. We prove this conjecture and give an explicit example to show that such a valuation need not be divisorial.

Keywords

singularitiesvaluationsnormalized volume

MSC classification

Primary: 14B05: Singularities
Secondary: 12J20: General valuation theory
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 4 , April 2018 , pp. 820 - 849
Copyright
© The Author 2018 

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