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 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.

dedicated to Dmitry Borisovich Fuchs

References in corpus (2)

• Newton polyhedra, tropical geometry and the ring of condition for $(C^{\ast }{)}^n$
• Note on the Grothendieck group of subspaces of rational functions and Shokurov's b-divisors

Cited by in corpus (1)

• Gorenstein algebras and toric bundles