We give a classification of all pairs (X, ξ) of Gorenstein del Pezzo surfaces X and vector fields ξ which are K-stable in the sense of Berman-Witt-Nyström and therefore are expected to admit a Kähler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kähler-Ricci soliton.

In this short note we determine the greatest lower bounds on Ricci curvature for all Fano T‐manifolds of complexity one, generalizing the result of Chi Li. Our method of proof is based on the work of Datar and Székelyhidi, using the description of complexity one special test configurations given by Ilten and Süß.

We calculate Chow quotients of some families of symmetric T-varieties. In complexity two we obtain new examples of Kähler–Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine the homeomorphism class of the orbit space of the compact torus action.

We calculate Chow quotients of some families of symmetric Tvarieties. In complexity two we obtain new examples of Kähler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine the homeomorpism class of the orbit space of the compact torus action.