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Combinatorial remarks on a classical theorem of Deligne

Emanuele Delucchi
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Abstract

We examine Deligne's classical proof of the asphericity of simplicial arrangements from the viewpoint of the combinatorics of the poset of regions of the arrangement. This turns out to be very natural. In particular, we show that an arrangement is simplicial only if it satisfies Deligne's property on positive paths, thus answering a question posed by Luis Paris.

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Emanuele Delucchi. 2006-11-24. Combinatorial remarks on a classical theorem of Deligne. https://arxiv.org/abs/math/0611759

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