Twisted Alexander polynomials of hypersurface complements

We study the twisted Alexander invariants of complex plane curves and higher dimensional hypersurfaces with possibly non-isolated singularities. We show that, generically, the twisted Alexander invariants for plane curves complements are torsion modules over some Laurent polynomial ring. As an application, the acyclity assumption required in Cogolludo and Florens work are satisfied.;Classical results on Alexander modules, for a hypersurface with non-isolated singularities in general position at infinity, will be generalized in the context of twisted invariants. The twisted Alexander modules are torsion modules and their orders divide the product of certain `local polynomials' defined by information from local link pairs at singular strata of a Whitney regular stratification of the hypersurface.