Volume 25, issue 4 (2021)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

Matthias Franz

Geometry & Topology 25 (2021) 2109–2144
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.

Keywords
toric variety, partial quotient, moment-angle complex, cohomology ring
Mathematical Subject Classification
Primary: 14M25, 57S12
Secondary: 14F45, 55N91