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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.
Received: November 4, 2019; in final form March 14, 2020; Published online March 20, 2020
Citation:
Kiumars Kaveh, Askold G. Khovanskii, “Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space”, SIGMA, 16 (2020), 016, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1553 https://www.mathnet.ru/eng/sigma/v16/p16
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Statistics & downloads: |
Abstract page: | 110 | Full-text PDF : | 18 | References: | 10 |
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