Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space

Abstract

We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space G/H. We also introduce the notion of a ring of complete intersections, firstly for a spherical homogeneous space and secondly for an arbitrary variety. Similarly to the ring of conditions of the torus, the ring of complete intersections of G/H admits a description in terms of volumes of polytopes.