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2021 The cohomology rings of smooth toric varieties and quotients of moment-angle complexes
Matthias Franz
Geom. Topol. 25(4): 2109-2144 (2021). DOI: 10.2140/gt.2021.25.2109

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.

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Matthias Franz. "The cohomology rings of smooth toric varieties and quotients of moment-angle complexes." Geom. Topol. 25 (4) 2109 - 2144, 2021. https://doi.org/10.2140/gt.2021.25.2109

Information

Received: 7 February 2020; Revised: 24 April 2020; Accepted: 23 May 2020; Published: 2021
First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.2109

Subjects:
Primary: 14M25 , 57S12
Secondary: 14F45 , 55N91

Keywords: cohomology ring , moment-angle complex , partial quotient , toric variety

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 4 • 2021
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