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arXiv · 1606.08894

Existence of valuations with smallest normalized volume

Harold 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 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. 2016-06-28. Existence of valuations with smallest normalized volume. https://doi.org/10.1112/s0010437x17008016

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