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arXiv · 0905.1284

First Milnor cohomology of hyperplane arrangements

Nero Budur·Alexandru Dimca·Morihiko Saito
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Abstract

We show a combinatorial formula for a lower bound of the dimension of the non-unipotent monodromy part of the first Milnor cohomology of a hyperplane arrangement satisfying some combinatorial conditions. This gives exactly its dimension if a stronger combinatorial condition is satisfied. We also prove a non-combinatorial formula for the dimension of the non-unipotent part of the first Milnor cohomology, which apparently depends on the position of the singular points. The latter generalizes a formula previously obtained by the second named author.

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Nero Budur, Alexandru Dimca, Morihiko Saito. 2010-05-17. First Milnor cohomology of hyperplane arrangements. https://arxiv.org/abs/0905.1284

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