Double coverings of arrangement complements and 2-torsion in Milnor fiber homology

We prove that the mod 2 Betti numbers of double coverings of a complex hyperplane arrangement complement are combinatorially determined. The proof is based on a relation between the mod 2 Aomoto complex and the transfer long exact sequence. Applying the above result to the icosidodecahedral arrangement (16 planes in the three-dimensional space related to the icosidodecahedron), we conclude that the first homology of the Milnor fiber has non-trivial 2-torsion.