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.

An appendix is added in this second version, where we use $p$-adic Hodge theory to prove that quite generally, whenever a $\G$-variety $X$ is defined over a number field, the number of rational points of its reductions modulo prime ideals can be used in certain cases to compute the equivariant Hodge-Deligne polynomial

References in corpus (1)

• The combinatorial part of the cohomology of a singular variety