Cohomology rings of quasitoric bundles

By Askold Khovanskii, Ivan Limonchenko, Leonid Monin. Filomat, 2021

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The classical Bernstein-Kushnirenko-Khovanskii theorem (or, the BKK theorem, for short) computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. In [PK92b], it was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the cohomology ring of a toric variety as a quotient of a ring of differential operators with constant coefficients by the annihilator of an explicit polynomial. In this paper we generalize this construction to the case of quasitoric bundles. These are fiber bundles with generalized quasitoric manifolds as fibers. First we obtain a generalization of the BKK theorem to this case. Then we use recently obtained descriptions of the graded-commutative algebras which satisfy Poincar? duality to give a description of cohomology rings of quasitoric bundles.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/88ba80a5f4d1e4eb071c0ca2fe3b343138f13c86