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.
 Publication:

SIGMA
 Pub Date:
 March 2020
 DOI:
 10.3842/SIGMA.2020.016
 arXiv:
 arXiv:1911.00118
 Bibcode:
 2020SIGMA..16..016K
 Keywords:

 BKK theorem; spherical variety; NewtonOkounkov polytope; ring of conditions;
 Mathematics  Algebraic Geometry;
 14M27;
 14M10
 EPrint:
 dedicated to Dmitry Borisovich Fuchs