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

Franz, Matthias¹

¹ Department of Mathematics, University of Western Ontario, London, ON, Canada

Geometry & topology, Tome 25 (2021) no. 4, pp. 2109-2144.

Résumé

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.

Détail

DOI : 10.2140/gt.2021.25.2109

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

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