The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

Abstract

Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a torsion product involving the corresponding Stanley-Reisner ring. We show that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. We rectify this by defining an explicit deformation of the canonical multiplication on the torsion product.

arXiv commentDedicated to Volker Puppe on the occasion of his 80th birthday. 26 pages; formulas (7.13) and (7.15) corrected

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Cited by in corpus (5)

• Dga models for moment-angle complexes
• The cohomology rings of real toric spaces and smooth real toric varieties
• Equivariant cohomological rigidity of certain $T$-manifolds
• Homotopy types of partial quotients for a certain case
• Cohomology of smooth toric varieties: naturality