Compactified Picard stacks over the moduli stack of stable curves with marked points

TL;DR

This paper constructs smooth, irreducible algebraic stacks that serve as a compactification of the universal Picard stack over the moduli space of stable n-pointed curves of genus g greater than 2, providing a new geometric framework.

Contribution

It introduces a new algebraic stack construction that compactifies the universal Picard stack over the moduli of stable curves with marked points for genus g > 2.

Findings

Stacks are smooth and irreducible.

Dimension of stacks is 4g-3+n.

Provides a meaningful geometric compactification.

Abstract

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n, yielding a geometrically meaningful compactification of the degree d universal Picard stack over the moduli stack of smooth curves with marked points.