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.
Subject
Algebra and Number Theory
Reference40 articles.
1. Sur une inégalité à la Minkowski pour les multiplicités, appendix to D. Eisenbud and H. I. Levine, The degree of a C ∞ map germ;Teissier;Ann. of Math. (2),1977
2. On a geometric interpretation of multiplicity
3. On multiplicities of graded sequences of ideals
4. Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
5. [Liu16] Y. Liu , The volume of singular Kähler–Einstein Fano varieties, Compositio Math., to appear. Preprint (2016), arXiv:1605.01034v2.
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