Alpha invariants of birationally rigid Fano threefolds

Abstract

We compute global log canonical thresholds, or equivalently alpha invariants, of birationally rigid orbifold Fano threefolds embedded in weighted projective spaces as codimension two or three. As an important application, we prove that most of them are weakly exceptional, $K$-stable and admit Kähler--Einstien metric.

38 pages