A basic topological invariant associated to an arrangement of hyperplanes is the fundamental group of their complement. A finite presentation for this group can be obtained from the braid monodromy of a generic plane section. A unifying framework for the study of arrangement groups is provided by their cohomology jumping loci: the characteristic and resonance varieties. These varieties, in turn, are connected in subtle ways to the combinatorics of the arrangement.

Keywords:

Hyperplane arrangements; characteristic variety; resonance variety; braid monodromy; fundamental group.

Lecture #10647

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