English

Existence of valuations with smallest normalized volume

Algebraic Geometry 2019-02-20 v3

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.

Cite

@article{arxiv.1606.08894,
  title  = {Existence of valuations with smallest normalized volume},
  author = {Harold Blum},
  journal= {arXiv preprint arXiv:1606.08894},
  year   = {2019}
}

Comments

26 pages, minor change made, comments welcome

R2 v1 2026-06-22T14:37:36.160Z