| A smooth curve over the complex numbers admits an Abel map, that is, an embedding into the complex torus known as the Jacobian, and the homomorphism on homology induced by the Abel map can be identified with the Poincaré Duality isomorphism. I will describe how this result extends to singular curves. In doing so, I will describe the compactified Jacobian of a curve with ordinary n-fold singularities, a result that is of independent interest. This work is joint with Kirsten Wickelgren. |