Compactified Jacobians of N\'eron type

Abstract

We characterize stable curves $X$ whose compactified degree-$d$ Jacobian is of N\'eron type. This means the following: for any one-parameter regular smoothing of $X$, the special fiber of the N\'eron model of the Jacobian of the generic fiber is isomorphic to a dense open subset of the degree-$d$ compactified Jacobian. It is well known that compactified Jacobians of N\'eron type have the best modular properties, and that they are endowed with a mapping property useful for applications.