Kiumars Kaveh, A. G. Khovanskii
Published 2010-07-24Version 1
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.
Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup
Actions of the derived group of a maximal unipotent subgroup on $G$-varieties
Describing the Jelonek set of polynomial maps via Newton polytopes
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