Describing toric varieties and their equivariant cohomology
Describing toric varieties and their equivariant cohomology
复制标题
描述环面簇及其等变上同调
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
M. Franz
中科院分区：
文献类型：
--
作者：
M. Franz
拓扑上，紧环变可以构造为识别空间：它们是紧环面与扇形的阶复积的商。我们给出了这一事实的详细证明，并将其推广到非紧情况，并得出了几个主要是上同调的结论。
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.