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 SIGMA, 2020, Volume 16, 016, 12 pp. (Mi sigma1553)

Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space

Kiumars Kaveha, Askold G. Khovanskiibc

a Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA
b Moscow Independent University, Moscow, Russia
c Department of Mathematics, University of Toronto, Toronto, Canada

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.

Keywords: BKK theorem, spherical variety, Newton–Okounkov polytope, ring of conditions.

 Funding Agency Grant Number National Science Foundation 1601303 Canadian Grant 156833-12 The first author is partially supported by a National Science Foundation grant (grant ID: 1601303). The second author is partially supported by the Canadian grant No. 156833-12.

DOI: https://doi.org/10.3842/SIGMA.2020.016

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ArXiv: 1911.00118
MSC: 14M27; 14M25; 14M10
Received: November 4, 2019; in final form March 14, 2020; Published online March 20, 2020
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Citation: Kiumars Kaveh, Askold G. Khovanskii, “Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space”, SIGMA, 16 (2020), 016, 12 pp.

Citation in format AMSBIB
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