Bernstein-Sato polynomials of hyperplane arrangements

Details Bernstein-Sato polynomials of hyperplane arrangements Bernstein-Sato polynomials of hyperplane arrangements

2006-02-23

arxiv.org/abs/math/0602527v5

Mathematics

Algebraic Geometry

20 pages

Scientific paper

We calculate the Bernstein-Sato polynomial (i.e. b-function) of a hyperplane arrangement with a reduced equation by using a generalization of Malgrange's formula together with a solution of Aomoto's conjecture due to Esnault, Schechtman, Viehweg. We show that the roots are greater than -2 and the multiplicity of -1 coincides with the (effective) dimension. We also get an estimate of the multiplicities of the roots in terms of the multiplicities of the arrangement at the dense edges, and give a method to calculate the b-function at least in the case of three variables with generic multiplicity at most 3 and with degree at most 7.

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