Obstructions to deforming maps from curves to surfaces

Abstract

This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and prove the unobstructedness of the deformation of such a map, even when the image is non-reduced. As an application, we give a simple but effective criterion for the vanishing of the obstructions to equisingular deformations of nodal curves on surfaces.