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28 March 2024
 
  » arxiv » 1007.4270

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Newton polytopes for horospherical spaces
Kiumars Kaveh ; A. G. Khovanskii ;
Date 24 Jul 2010
AbstractA 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.
Source arXiv, 1007.4270
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