Generalized virtual polytopes and quasitoric manifolds

TL;DR

This paper develops a topological framework for volume polynomials of generalized virtual polytopes, leading to new descriptions of cohomology rings of generalized quasitoric manifolds and a topological version of the BKK Theorem.

Contribution

It introduces a novel topological approach to volume polynomials and extends classical theorems to generalized quasitoric manifolds.

Findings

Topological description of volume polynomials for virtual polytopes

A topological version of the BKK Theorem

Descriptions of cohomology rings for generalized quasitoric manifolds

Abstract

In this paper 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 BKK Theorem, the Stanley-Reisner and Pukhlikov-Khovanskii type descriptions for cohomology rings of generalized quasitoric manifolds.