Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements

2010/06/17 by Alexandru Dimca, Dimca, Alexandru, G Lehrer +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.1006.3462

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.

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• Purity of generalized affine Springer fibers from generic planar curve singularities

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