Christophe Eyral

Title: 
The Zariski multiplicity conjecture for deformations of homogeneous 
hypersurfaces with line singularities

Abstract: 
The Zariski multiplicity conjecture says that if {f_t} is a family 
of complex hypersurface singularities with constant topological type, 
then {f_t} is equimultiple. Gabrièlov and Kouchnirenko showed that 
this conjecture is true in the special case of families of isolated 
singularities with f_0 homogeneous. I will discuss the same question 
as Gabrièlov and Kouchnirenko for the simplest class of hypersurfaces 
with non-isolated singularities, namely the hypersurfaces with line 
singularities.