Cohomology Rings of Toric Bundles and the Ring of Conditions.

The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding system of Newton polytopes. In Pukhlikov and Khovanskiĭ (Algebra i Analiz 4(4):188-216, 1992), Pukhlikov and the second author noticed that the cohomology ring of smooth projective toric varieties over can be computed via the BKK Theorem. This complemented the known descriptions of the cohomology ring of toric varieties, like the one in terms of Stanley-Reisner algebras.