Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements

Alexandru Dimca (1) , Gus Lehrer (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 School of Mathematics and statistics [Sydney]

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.

Domaines: Géométrie algébrique [math.AG]

Alexandru Dimca, Gus Lehrer. Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements. Configuration Spaces, Geometry, Combinatorics and Topology, 2011, Pisa, Italy. pp.231-253. ⟨hal-00940208⟩