Newton polytopes for horospherical spaces

Details Newton polytopes for horospherical spaces Newton polytopes for horospherical spaces

2010-07-24

arxiv.org/abs/1007.4270v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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.

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