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SIGMA 16 (2020), 016, 12 pages arXiv:1911.00118
https://doi.org/10.3842/SIGMA.2020.016
Contribution to the Special Issue on Algebra, Topology, and Dynamics in Interaction in honor of Dmitry Fuchs
Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space
Kiumars Kaveh a and Askold G. Khovanskii bc
a) Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
b) Department of Mathematics, University of Toronto, Toronto, Canada
c) Moscow Independent University, Moscow, Russia
Received November 04, 2019, in final form March 14, 2020; Published online March 20, 2020
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.
Key words: BKK theorem; spherical variety; Newton-Okounkov polytope; ring of conditions.
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