Twisted Alexander polynomials of Plane Algebraic Curves

Details Twisted Alexander polynomials of Plane Algebraic Curves Twisted Alexander polynomials of Plane Algebraic Curves

2005-04-18

arxiv.org/abs/math/0504356v2

Mathematics

Geometric Topology

16 pages, no figures

Scientific paper

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is given by the determinant of its Blanchfield intersection form. Specializing in the classical case, this gives a geometrical interpretation of Libgober's divisibility Theorem. We calculate twisted polynomials for some algebraic curves and show how they can detect Zariski pairs of equivalent Alexander polynomials and that they are sensitive to nodal degenerations.

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