The cone of numerically effective divisors for spherical varieties and Gale duality

In the talk I will give a brief introduction to the theory of G-equivariant embeddings of spherical varieties, which can be described in terms of combinatorial data the so-called colored fans, which generalize the fans for toric varieties. Then I will explain how to describe the cone of numerically effective divisors. In the classical literature this cone is described in terms of the convex piecewise-linear functions on the colored fan. Recently it has become clear that in many problems of toric geometry the so-called Gale duality arises in a natural way. I will tell how Gale duality arises in the description of the cone of numerically-effective divisors for spherical varieties (which is the closure of the cone of ample divisors) and the description of the Picard group.