Lectures series "Aspects of Singularities".
 

1999, by Victor Goryunov

2000, by Anatoly Libgober

 
 Year 2000 lectures, by Anatoly Libgober

May: 11. Hours: 14h. Place: Salle Kampé de Fériet, M2.
May: 12, 26. Hours: 15h. Place: Salle Duhem, M3.

Series of lectures on :

Topology of the complements to projective singular
curves and hypersurfaces.

Abstract:
The main problem in the topology of plane singular curves
is the classification of families of curves with the same
local type of singularities. Among invariants of such families
are fundamental groups and the Alexander invariants of the
complements. The goal of the series is to discuss main problems
in the study of plane singular curves and how Alexander
invariants depend on the local type of singularities and their
geometry as a subset of the projective plane. It turns out that
Alexander invariants of complements are affected by new Hodge
theoretical invariants of local singularities. Some of the aspects
of the theory of Alexander invariants can be extended to the study
of hypersurfaces with isolated singularities in projective spaces
yielding information about certain homotopy groups of the complements
and their dependence on geometry of singularities.