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Abstract. We examine complements (inside products of a smooth projective complex curve of arbitrary genus) of unions of diagonals indexed by the edges of an arbitrary simple graph. We use Orlik-Solomon models associated to these quasi-projective manifolds to compute pairs of analytic germs at the origin, both for rank 1 and 2 representation varieties of their fundamental groups, and for degree 1 topological Green-Lazarsfeld loci. As a corollary, we describe all regular surjections with connected generic fiber, defined on the above complements onto smooth complex curves of negative Euler characteristic. We show that the nontrivial part at the origin, for both rank 2 representation varieties and their degree 1 jump loci, comes from curves of general type, via the above regular maps. We compute explicit finite presentations for the Malcev Lie algebras of the fundamental groups, and we analyze their formality properties.

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We compute the combinatorial Aomoto-Betti numbers β p ÔAÕ of a complex reflection arrangement. When A has rank at least 3, we find that β p ÔAÕ 2, for all primes p. Moreover, β p ÔAÕ 0 if p 3, and β 2 ÔAÕ 0 if and only if A is the Hesse arrangement. We deduce that the multiplicity e d ÔAÕ of an order d eigenvalue of the monodromy action on the first rational homology of the Milnor fiber is equal to the corresponding Aomoto-Betti number, when d is prime. We give a uniform combinatorial characterization of the property e d ÔAÕ 0, for 2 d 4. We completely describe the monodromy action for full monomial arrangements of rank 3 and 4. We relate e d ÔAÕ and β p ÔAÕ to multinets, on an arbitrary arrangement.