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The
cohomology rings of smooth toric varieties and quotients of
moment-angle complexes
Matthias Franz |
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Geometry & Topology 25 (2021) 2109–2144
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Abstract |
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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 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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Keywords
toric variety, partial quotient, moment-angle complex,
cohomology ring
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Mathematical Subject Classification
Primary: 14M25, 57S12
Secondary: 14F45, 55N91
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References |
Publication
Received: 7 February 2020
Revised: 24 April 2020
Accepted: 23 May 2020
Published: 12 July 2021
Proposed: Frances Kirwan
Seconded: Dan Abramovich, Anna Wienhard
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Authors |
| Matthias Franz | |
| Department of Mathematics University of Western Ontario London, ON Canada |
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