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.

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

References in corpus (4)

• Equivariant geometry and the cohomology of the moduli space of curves
• The cohomology rings of homogeneous spaces
• Multiplication structure of the cohomology ring of real toric spaces
• Categorical aspects of toric topology

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