Boundary complexes and weight filtrations
Boundary complexes and weight filtrations
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边界复合体和权重过滤
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发表时间：
2011
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通讯作者：
S. Payne
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作者：
S. Payne
我们研究了代数簇紧化的对数分辨率中边界因子的对偶复形，并表明这些复形的同伦类型独立于所有选择。受非阿基米德几何最新发展的启发，我们考虑了这些边界复形与奇异上同调和紧支撑上同调上的权重过滤之间的关系，并将其应用到孤立奇点分辨率的对偶复形上，从而推广了 Stepanov 和 Thuillier 的结果。
We study the dual complexes of boundary divisors in log resolutions of compactifications of algebraic varieties and show that the homotopy types of these complexes are independent of all choices. Inspired by recent developments in nonarchimedean geometry, we consider relations between these boundary complexes and weight filtrations on singular cohomology and cohomology with compact supports, and give applications to dual complexes of resolutions of isolated singularities that generalize results of Stepanov and Thuillier.