On the integral cohomology of smooth toric varieties

dc.creatorFranz, Matthias
dc.date2003-08-27
dc.date.accessioned2026-07-07T08:37:11Z
dc.date.available2026-07-07T08:37:11Z
dc.descriptionLet $X_Σ$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $Σ$, computes the integral cohomology of $X_Σ$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_Σ$ is formal.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0308253
dc.identifierhttp://arxiv.org/abs/math/0308253
dc.identifierProc. Steklov Inst. Math. 252 (2006), 53-62 [substantially revised version]
dc.identifierdoi:10.1134/S008154380601007X
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140315
dc.subjectAlgebraic Topology
dc.subjectAlgebraic Geometry
dc.subject14M25, 55N10 (primary), 14C15, 55N91 (secondary)
dc.titleOn the integral cohomology of smooth toric varieties
dc.typetext

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