Boundedness of log Fano cone singularities and discreteness of local volumes

Abstract

We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence, we show that the set of local volumes of klt singularities of a fixed dimension has zero as the only accumulation point.

27 pages. Comments are welcome! v2: added Theorem 1.3 and Section 4 on boundedness of minimal log discrepancies of Kollár components when volume is bounded away from zero

Cited by in corpus (1)

• Boundedness of stable minimal models with klt singularities