A valuative criterion of K-polystability

Abstract

For any log Fano pair with a torus action, we associate a computable invariant to it, such that the pair is (weighted) K-polystable if and only if this invariant is greater than one. As an application, we present examples of Fano varieties admitting $g$-solitons for any weight function $g$.

27 pages, comments are very welcome. v2: accepted version. To appear in TAMS