Twisted Alexander polynomials of plane algebraic curves

Abstract

In the present paper, Alexander polynomials of plane algebraic curves twisted by linear representations are considered. They are shown to divide the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is given by the determinant of the Blanchfield intersection form. Specializing to the classical case, this gives a divisibility formula in the sense of Libgober's divisibility theorem. Examples of twisted polynomials for some algebraic curves are explicitly calculated showing that they can detect Zariski pairs of equivalent Alexander polynomials and that they are sensitive to nodal degenerations.