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.
Keywords
Cite
@article{arxiv.1006.3462,
title = {Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements},
author = {Alexandru Dimca and Gus Lehrer},
journal= {arXiv preprint arXiv:1006.3462},
year = {2011}
}
Comments
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