Enrique Artal Bartolo (Zaragoza, Spain)

Tpology of Polynomials and Low Dimensional Algebraic Geometry

Lecture 1: Local singularities
Puiseux expansions;
Braids and algebraic links;
Pencils of Curves.
Lecture 2: Topology of polynomials
bifurcation set;
links at infinity;
characterization of polynomials good-at-infinity;
tame polynomials and morsifications.
Lecture 3: Zariski-van Kampen theorem and braid monodromy
Zariski-van Kampen method;
Braid monodromy;
Embedded topology of plane curves.
Lecture 4: Discriminant method for tame polynomials
Discriminant of the polar map;
Braid and classical monodromy;


1. V.I. Arnol'd, S.M. Gusein-Zade, and A.N. Varchenko, Singularities of differentiable maps. Vol. II, Birkhauser Boston Inc., Boston, MA, 1988.
2. E. Artal, J. Carmona, and J.I. Cogolludo, Braid monodromy and topology of plane curves, Duke Math. J. 118 (2003), no. 2, 261-278.
3. M. Escario, Discriminant method for the homological monodromy of tame polynomials, math.AG/0602297.