Title: Algebraic moment polytopes of polarized spherical varieties

Speaker: Kyeong-Dong Park(Gyeongsang National University)

Abstract: Spherical varieties form a remarkable class of algebraic varieties equipped with an action of a reductive algebraic group G, which contains several important classes such as toric varieties, rational homogeneous varieties, group embeddings, horospherical varieties, symmetric varieties, and wonderful varieties. They are classified by combinatorial objects called colored fans, which generalize fans appearing in the classification of toric varieties.

The algebraic moment polytope of a polarized spherical variety is a polytope encoding the structure of representations of G on the spaces of sections of tensor powers of an ample line bundle. Many geometric properties of polarized spherical varieties can be described from the algebraic moment polytopes. In particular, we have a combinatorial criterion for K-stability of a smooth Fano spherical variety in terms of the barycenter of its moment polytope with respect to the Duistermaat-Heckman measure and some data associated to the corresponding spherical homogeneous space.