Perversity, duality, and arrangements in C3

In this paper, we use the perversity and self-duality of the sheaf of vanishing cycles to obtain previously unknown bounds on the Betti numbers of the Milnor fibre of a central hyperplane arrangement in C3. Moreover, we obtain restrictions on the monodromy action on cohomology which yield number-theoretic constraints on the Betti numbers of the Milnor fibre.