On the integral cohomology of smooth toric varieties
| dc.creator | Franz, Matthias | |
| dc.date | 2003-08-27 | |
| dc.date.accessioned | 2026-07-07T08:37:11Z | |
| dc.date.available | 2026-07-07T08:37:11Z | |
| dc.description | Let $X_Σ$ 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.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308253 | |
| dc.identifier | http://arxiv.org/abs/math/0308253 | |
| dc.identifier | Proc. Steklov Inst. Math. 252 (2006), 53-62 [substantially revised version] | |
| dc.identifier | doi:10.1134/S008154380601007X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140315 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M25, 55N10 (primary), 14C15, 55N91 (secondary) | |
| dc.title | On the integral cohomology of smooth toric varieties | |
| dc.type | text |