Room P3.10, Mathematics Building

Thibaut Delcroix, Institut Fourier
K-stability of Fano spherical varieties

The resolution of the Yau-Tian-Donaldson conjecture for Fano manifolds, that is, the equivalence of the existence of Kähler-Einstein metrics with K-stability, raises the question of determining when a given Fano manifold is K-stable.

I will present a combinatorial criterion of K-stability for Fano spherical manifolds. These form a very large class of almost-homogeneous manifolds, containing toric manifolds, homogeneous toric bundles, and classes of manifolds for which the Kähler-Einstein existence question was not solved yet, for example equivariant compactifications of (complex) symmetric spaces.