归结的关联组合
Incidence combinatorics of resolutions
摘要：
我们介绍的概念组合爆破，建筑集，和套任意满足半格。这给出了一个共同的抽象框架发生在德Concini-Procesi模型的子空间安排和决议的环面品种的奇异性的背景下的发病率组合。我们的主要定理指出，一个序列的组合爆破，规定的建设集在线性扩张兼容的顺序，给出了面偏序集的相应单纯复形套。作为应用程序，我们跟踪的发病率组合通过每一步的德Concini-Procesi模型建设，我们引入的概念，建设集和嵌套集的上下文的环面品种。还有其他几个例子，如模型的分层流形和某些分次代数与有限格，我们的组合框架已投入工作，我们在本文的最后提出了一个大纲。
英文摘要：
We introduce notions of combinatorial blowups, building sets, and nested sets for arbitrary meet-semilattices. This gives a common abstract framework for the incidence combinatorics occurring in the context of De Concini-Procesi models of subspace arrangements and resolutions of singularities in toric varieties. Our main theorem states that a sequence of combinatorial blowups, prescribed by a building set in linear extension compatible order, gives the face poset of the corresponding simplicial complex of nested sets. As applications we trace the incidence combinatorics through every step of the De Concini-Procesi model construction, and we introduce the notions of building sets and nested sets to the context of toric varieties. There are several other instances, such as models of stratified manifolds and certain graded algebras associated with finite lattices, where our combinatorial framework has been put to work; we present an outline in the end of this paper.
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