Hodge-deligne equivariant polynomials and monodromy of hyperplane arrangements

Abstract

We investigate the interplay between the monodromy and the Deligne mixed Hodge structure on the Milnor fiber of a homogeneous polynomial. In the case of hyperplane arrangement Milnor fibers, we obtain a new result on the possible weights. For line arrangements, we prove in a new way the fact due to Budur and Saito that the spectrum is determined by the weak combinatorial data, and show that such a result fails for the Hodge-Deligne polynomials. In an appendix, we also establish a connection between the Hodge-Deligne polynomials and rational points over finite fields.