Existence of valuations with smallest normalized volume

Published 28 Jun 2016 in math.AG | (1606.08894v3)

Abstract: Li introduced the normalized volume of a valuation due to its relation to K-semistability. He conjectured that over a klt singularity there exists a valuation with smallest normalized volume. We prove this conjecture and provide an example to show that such a valuation need not be divisorial.

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Harold Blum

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