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