On boundedness of singularities and minimal log discrepancies of Kollár components, II

Abstract

We show that a set of K-semistable log Fano cone singularities is bounded if and only if their local volumes are bounded away from zero, and their minimal log discrepancies of Kollár components are bounded from above. As corollaries, we confirm the boundedness conjecture for K-semistable log Fano cone singularities in dimension three, and show that local volumes of 3-dimensional klt singularities only accumulate at zero.

23 pages. Comments are welcome! v2: minor revision. To appear in Geometry and Topology

References in corpus (1)

• No semistability at infinity for Calabi-Yau metrics asymptotic to cones

Cited by in corpus (1)

• Stable degeneration of families of klt singularities with constant local volume