Newton polytopes for horospherical spaces
Algebraic Geometry
2010-07-27 v1
Abstract
A subgroup H of a reductive group G is horospherical if it contains a maximal unipotent subgroup. We describe the Grothendieck semigroup of invariant subspaces of regular functions on G/H as a semigroup of convex polytopes. From this we obtain a formula for the number of solutions of a generic system of equations on G/H in terms of mixed volume of polytopes. This generalizes Bernstein-Kushnirenko theorem from toric geometry.
Cite
@article{arxiv.1007.4270,
title = {Newton polytopes for horospherical spaces},
author = {Kiumars Kaveh and A. G. Khovanskii},
journal= {arXiv preprint arXiv:1007.4270},
year = {2010}
}
Comments
17 pages