Compactified Jacobians of N\'eron type

TL;DR

This paper characterizes stable curves whose compactified degree-d Jacobians exhibit Néron type properties, ensuring optimal modular behavior and a key mapping property useful for various applications.

Contribution

It provides a characterization of stable curves with Néron type compactified Jacobians, linking geometric properties to modular and mapping features.

Findings

Identifies conditions for stable curves to have Néron type Jacobians

Shows Néron type Jacobians have optimal modular properties

Establishes a connection between curve stability and Jacobian behavior

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.