标题： 链丛与复环面簇的交空间 显示英文标题

标题： Link Bundles and Intersection Spaces of Complex Toric Varieties

摘要： 存在几种满足广义庞加莱对偶性的奇异空间同调理论，包括Goresky-MacPherson的交集同调、Cheeger的$L^2$上同调以及交集空间的同调。 交集同调和$L^2$上同调对于环面簇是已知的。 在这里，我们计算复数3维环面簇的交集空间的有理同调，并将其与交集同调进行比较。 为了实现这一点，我们分析这些簇的单元结构和拓扑分层，并确定其奇点链在上的相容结构。 特别是，我们计算了3维环面簇中链的同调。 我们发现使用有理同调分层的概念很方便。 结果表明，环面簇的交集空间同调与其交集同调不同，不是组合不变量，因此保留了关于定义扇形的更精细的信息。 显示英文摘要

摘要： There exist several homology theories for singular spaces that satisfy generalized Poincar\'e duality, including Goresky-MacPherson's intersection homology, Cheeger's $L^2$ cohomology and the homology of intersection spaces. The intersection homology and $L^2$ cohomology of toric varieties is known. Here, we compute the rational homology of intersection spaces of complex 3-dimensional toric varieties and compare it to intersection homology. To achieve this, we analyze cell structures and topological stratifications of these varieties and determine compatible structures on their singularity links. In particular, we compute the homology of links in 3-dimensional toric varieties. We find it convenient to use the concept of a rational homology stratification. It turns out that the intersection space homology of a toric variety, contrary to its intersection homology, is not combinatorially invariant and thus retains more refined information on the defining fan.