arXiv math/03082532003-08-27math.ATmath.AG

On the integral cohomology of smooth toric varieties

Matthias Franz

备注：: 10 pages
发表信息：: Proc. Steklov Inst. Math. 252 (2006), 53-62 [substantially revised version]
DOI：: 10.1134/S008154380601007X

英文摘要：

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.

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