Singularities of secant maps on closed plane curves

Abstract

We study the singularities of secant maps associated to pairs of plane curves providing their geometrical interpretation up to codimension 2. We show that for most pairs of closed plane curves the secant map is a stable map from the torus to the plane. We determine the isotopy type of the singular set of the secant map associated to pairs of convex closed curves in terms of their Whitney indices.