Dmitry Kerner: On some geometric aspects of the discriminant of plane curves.

abstract: Consider the complete linear system of complex plane algebraic curves of fixed degree. The generic such curve is smooth, the set of singular curves is a hypersurface, called the discriminant. The discriminant is stratified by the singular types of the curves.

This stratification has been classicaly studied (since the 19'th century). There are many research directions: *singularities of the closures of strata, their resolutions *properties of the embeddings of the strata into the space of complete linear system *cohomology rings of the strata, of the resolved closures *relations to enumerative geometry, Gromov-Witten etc. .....

I will give a brief introduction to the field, stating mostly the classical results.