Existence of valuations with smallest normalized volume

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.

26 pages, minor change made, comments welcome

References in corpus (1)

• Which powers of holomorphic functions are integrable?

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