复曲面簇及其等变上同调的刻画
Describing toric varieties and their equivariant cohomology
摘要：
拓扑上，紧环面簇可以被构造为标识空间：它们是紧环面与扇的序复形的乘积的乘积。我们给出了一个详细的证明这一事实，将其扩展到非紧的情况下，并得出几个，主要是上同调的结论。特别是，我们表明，等变积分上同调的环面品种可以描述的分段多项式的风扇，如果普通的积分上同调集中在偶数度。这将Bahri-Franz-Ray的一个结果推广到了非紧情形。我们还研究了积分上同调中的挠率现象。
英文摘要：
Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even degrees. This generalizes a result of Bahri-Franz-Ray to the non-compact case. We also investigate torsion phenomena in integral cohomology.
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