This work contains an extended version of a course given in held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees) and the notion of essential coordinate components.
In this work, we compute the Alexander invariants at infinity of a complex polynomial in two variables by means of its resolution and also by means of the Eisenbud-Neumann diagram of the generic link at infinity of the polynomial.
In this work, we describe the historic links between the study of -dimensional manifolds (specially knot theory) and the study of the topology of complex plane curves with a particular attention to the role of braid groups and Alexander-like invariants (torsions, different instances of Alexander polynomials). We finish with detailed computations in an example.
Soit où et sont des applications
polynomiales. Nous établissons le lien qui existe entre le polygone de Newton de la
courbe réunion du discriminant et du lieu de non-propreté de et la topologie des
entrelacs à l’infini des courbes affines et . Nous en déduisons
alors des conséquences liées à la conjecture du jacobien.
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