摘要翻译：
我们建立了一个公式，它将简单法线交因子(SNC)D$上的各种束的上同调分解成对偶复数D_telta(D)$的单纯上同调。这个预集精确地由$d$的分量及其交点上相应的上同调数据组成。我们利用这个公式给出了SNC因子的Hodge分解，并研究了toric设置。我们还猜想了具有SNC支持的有效非约简因子的一个公式的存在性，并证明了这将意味着与孤立有理奇点的分解有关的对偶复的更高单纯上同调的消失。
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英文标题：
《On the cohomology of a simple normal crossings divisor》
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作者：
Parsa Bakhtary
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor (SNC) $D$ in terms of the simplicial cohomologies of the dual complex $\Delta(D)$ with coefficients in a presheaf of vector spaces. This presheaf consists precisely of the corresponding cohomology data on the components of $D$ and on their intersections. We use this formula to give a Hodge decomposition for SNC divisors and investigate the toric setting. We also conjecture the existence of such a formula for effective non-reduced divisors with SNC support, and show that this would imply the vanishing of the higher simplicial cohomologies of the dual complex associated to a resolution of an isolated rational singularity.
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PDF链接：
https://arxiv.org/pdf/0811.2246