  In this note we determine the Bernstein-Sato polynomial $b_Q(s)$ of a generic
central arrangement $Q=\prod_{i=1}^kH_i$ of hyperplanes. We establish a
connection between the roots of $b_Q(s)$ and the degrees of the generators for
the top cohomology of the corresponding Milnor fiber. This connection holds for
all homogeneous polynomials. We also introduce certain subschemes of the
arrangement determined by the roots of $b_Q(s)$.
