Compactified Jacobians of Néron type

Abstract

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