A two-step approach to Chow quotients

Abstract

The Chow quotient of a projective variety by the action of a complex torus is known to have a very complicated geometry, even in the case of simple varieties, such as rational homogeneous varieties. In this paper we propose an approach in which the geometry of the Chow quotient is encoded in a projective toric variety and a finite subgroup of its birational automorphisms. We then illustrate how to apply our strategy in the case of some particular rational homogeneous varieties.