Cohomology of smooth toric varieties: naturality

Abstract

Building on the recent computation of the cohomology rings of smooth toric varieties and partial quotients of moment-angle complexes, we investigate the naturality properties of the resulting isomorphism between the cohomology of such a space and the torsion product involving the Stanley-Reisner ring. If 2 is invertible in the chosen coefficient ring, then the isomorphism is natural with respect to toric morphisms, which for partial quotients are defined in analogy with toric varieties. In general there are deformation terms that we describe explicitly.

arXiv comment36 pages; introduction expanded, minor changes

References in corpus (6)

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• Describing toric varieties and their equivariant cohomology
• The cohomology rings of homogeneous spaces
• The cohomology rings of smooth toric varieties and quotients of moment-angle complexes
• Homotopy Gerstenhaber algebras are strongly homotopy commutative
• Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces