Hyperplane arrangements and the Gauss map of a pencil
Abstract
We show that the coefficients of the characteristic polynomial of a central hyperplane arrangement A, coincide with the multidegrees of the Gauss map of a pencil of hypersurfaces naturally associated to A. As a consequence, we obtain a proof of the Heron-Rota-Welsh conjecture for matroids representable over a field of characteristic zero.
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