Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.Pukhlikov and the second author noticed that the
cohomology ring of smooth projective toric varieties over $\mathbb{C}$ 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.
  Sankaran and Uma generalized the "Stanley-Reisner description" to the case of
toric bundles, i.e. equivariant compactifications of (not necessarily
algebraic) torus principal bundles. We provide a description of the cohomology
ring of toric bundles which is based on a generalization of the \BKK Theorem,
and thus extends the approach by Pukhlikov and the second author. Indeed, for
every cohomology class of the base of the toric bundle, we obtain a BKK-type
theorem. Furthermore, our proof relies on a description of graded-commutative
algebras which satisfy Poincar\'e duality.
  From this computation of the cohomology ring of toric bundles, we obtain a
description of the ring of conditions of horospherical homogeneous spaces as
well as a version of Brion-Kazarnovskii theorem for them. We conclude the
manuscript with a number of examples. In particular, we apply our results to
toric bundles over a full flag variety $G/B$. The description that we get
generalizes the corresponding description of the cohomology ring of toric
varieties as well as the one of full flag varieties $G/B$ previously obtained
by Kaveh.

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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys