Juan Viu Sos (ICMC-USP)

Tuesday, April 18th, 10:20, Room 4-111

**Title**: Configurations of points and topology of real line arrangements

**Abstract**. A classical problem of line arrangements on the complex projective plane is the study of the influence of the combinatorics (i.e. incidence relations between lines) over its topology. At this time, there exist only three examples of pairs of combinatorially equivalent line arrangements with different topology (called Zariski pairs). Among them, only one pair admits real equations, and we do not know if this pair can be distinguished by the respective fundamental groups of the complementary of the arrangements.

In this talk, we present a method to distinguish Zariski pairs admitting real equations. This method consists on the weight counting of points of the dual configuration, located in particular chambers of the real projective plane. Using this point of view, we construct in GeoGebra a Zariski pair of 13 lines with rational coefficients. We also show that the fundamental groups associated to this pair are non-isomorphic.

This is a joint work with B. Guerville-Ballé (Tokyo Gakugei University).