Authors: Limonchenko, Ivan 
Monin, Leonid V.
Khovanskii, Askold G.
Title: Generalized Virtual Polytopes and Quasitoric Manifolds
Journal: Proceedings of the Steklov Institute of Mathematics
Volume: 318
First page: 126
Last page: 149
Issue Date: 2022
Rank: M23
ISSN: 0081-5438
DOI: 10.1134/S0081543822040095
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.
Publisher: Springer Link

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