Alpha invariants of birationally bi-rigid Fano 3-folds I (Q2024100)

The article is devoted to the computation of global log canonical thresholds -- equivalently, \(\alpha\)-invariants -- of certain classes of non birationally rigid Fano threefolds of index 1 with terminal singularities, embedded in weighted projective 5-spaces as quasi-smooth, well-formed complete intersections of codimension 2. It is established that general bi-rigid members of certain of the 85 existing families of such weighted complete intersections have global log canonical thresholds equal to 1. In particular, they are K-stable and admit orbifold Kähler-Einstein metrics. In another direction, applications to the construction of new examples of super-rigid affine Fano 4-folds are given.