Equisingular moduli of singular curves
Frederick van der Wyck, Harvard

A nodal curve is determined by its normalization, marked with the points lying over its nodes. On the other hand, to specify a curve with more general singularities, it is not enough to give the pointed normalization and the isomorphism types of the singularities. We discuss the relevant deformation theory, introduce the notion of crimping a smooth curve and define and study moduli spaces of curves all of which have a given singularity.