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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 318, Pages 139–165
DOI: https://doi.org/10.4213/tm4272 (Mi tm4272) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalized Virtual Polytopes and Quasitoric Manifolds

Ivan Yu. Limonchenkoa, Leonid V. Moninb, Askold G. Khovanskiicd

a National Research University Higher School of Economics, Pokrovskii bul. 11, Moscow, 109028 Russia
b Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
c Independent University of Moscow, Bol'shoi Vlas'evskii per. 11, Moscow, 119002 Russia
d Department of Mathematics, University of Toronto, 40 St. George St., Toronto, M5S 2E4, Canada
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DOI: https://doi.org/10.4213/tm4272
Abstract: We develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the Bernstein–Kushnirenko theorem as well as Stanley–Reisner and Pukhlikov–Khovanskii type descriptions for the cohomology rings of generalized quasitoric manifolds.
Keywords: quasitoric manifold, star-shaped sphere, virtual polytope, multi-fan, multi-polytope, moment–angle complex, Stanley–Reisner ring.
Funding agency Grant number
HSE Basic Research Program
Canadian Grant 156833-17
The work of the first author was performed within the framework of the HSE University Basic Research Program. The third author was supported in part by the Canadian Grant no. 156833-17.
Received: March 15, 2022
Revised: April 12, 2022
Accepted: May 11, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 318, Pages 126–149
DOI: https://doi.org/10.1134/S0081543822040095
Bibliographic databases:
Document Type: Article
UDC: 515.145
MSC: 57S12, 13F55, 55N45
Language: Russian
Citation: Ivan Yu. Limonchenko, Leonid V. Monin, Askold G. Khovanskii, “Generalized Virtual Polytopes and Quasitoric Manifolds”, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Collected papers, Trudy Mat. Inst. Steklova, 318, Steklov Math. Inst., Moscow, 2022, 139–165; Proc. Steklov Inst. Math., 318 (2022), 126–149
Citation in format AMSBIB
\Bibitem{LimMonKho22}
\by Ivan~Yu.~Limonchenko, Leonid~V.~Monin, Askold~G.~Khovanskii
\paper Generalized Virtual Polytopes and Quasitoric Manifolds
\inbook Toric Topology, Group Actions, Geometry, and Combinatorics. Part~2
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 318
\pages 139--165
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4272}
\crossref{https://doi.org/10.4213/tm4272}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 318
\pages 126--149
\crossref{https://doi.org/10.1134/S0081543822040095}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142110904}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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