Twisted Alexander polynomials of Plane Algebraic Curves

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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.
16 pages, no figures

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Geometric Topology, Algebraic Geometry, 57M05,57Q10,58K65,14H30,14B05,55N33

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http://salesiana.dossiersoluciones.com/handle/123456789/74934

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504356
 http://arxiv.org/abs/math/0504356

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arXiv