  We define twisted Alexander polynomials of a complex hypersurface with
arbitrary singularities. These generalize the classical Alexander polynomials
of high dimensional hypersurfaces and the twisted Alexander polynomial of plane
curves. We recover the classical torsionness and divisibility results, which
say that, under certain assumptions, the twisted Alexander modules of a complex
hypersurface are torsion modules, and that their orders, the twisted Alexander
polynomials, divide the product of certain `local polynomials' defined in terms
of the topology near singularities.
