Combinatorial remarks on a classical theorem of Deligne

Details Combinatorial remarks on a classical theorem of Deligne Combinatorial remarks on a classical theorem of Deligne

2006-11-24

arxiv.org/abs/math/0611759v1

Mathematics

Combinatorics

9 pages, 2 figures

Scientific paper

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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