Singularities and K-stability

[摘要] We study invariants of singularities that have arisen in connection withthe K-stability of Fano varieties. The first invariant we consider is Li;;s normalized volume function on the space ofvaluations over a klt singularitiy. Proving a conjecture of Li, we show that there always exists a valuation over a klt singularity with smallest normalized volume. Next, we present joint work with Mattias Jonsson on the log canonical and stability thresholds of a line bundle. The latter notion generalizes an invariant recently introduced by Fujita and Odaka, and can be used to characterize when a Fano variety is K-semistable or uniformly K-stable. We express the two thresholds as infima of certain functionals on the space of valuations and systematically study these invariants.

[发布机构] University of Michigan

[效力级别] log canonical thresholds

[关键词] singularities;log canonical thresholds;valuations;K-stability;Mathematics;Science;Mathematics