Universal N\'eron models for curves with marked points

TL;DR

This paper constructs universal Néron models for families of curves with sections, extending the theory to smooth families with planar singularities over Dedekind schemes using compactified Jacobians.

Contribution

It provides a new construction of universal Néron models for certain families of curves, combining compactified Jacobians and recent results to cover smooth families with planar singularities.

Findings

Universal Néron models exist for smooth families with planar singularities.

The construction uses universal compactified Jacobians over moduli stacks.

The approach applies over Dedekind schemes.

Abstract

We consider the problem of constructing universal N\'eron models for families of curves with sections. By applying a construction of the author of universal compactified Jacobians over the moduli stack of reduced curves with markings and a result by J. Kass, we get a positive answer for smooth families of curves with planar singularities over Dedekind schemes.