Alpha invariants of birationally rigid Fano threefolds
  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 K\"{a}hler--Einstien metric. 
In-Kyun Kim, Takuzo Okada, Joonyeong Won
math.AG