First Milnor cohomology of hyperplane arrangements

Details First Milnor cohomology of hyperplane arrangements First Milnor cohomology of hyperplane arrangements

2009-05-08

arxiv.org/abs/0905.1284v6

Mathematics

Algebraic Geometry

15 pages, final version

Scientific paper

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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