Compactified Picard stacks over $\bar{\mathcal M}_g$

TL;DR

This paper develops a functorial approach to compactify the relative degree d Picard variety over the moduli space of stable curves, providing new insights into the structure of algebraic stacks in this context.

Contribution

It introduces a novel algebraic stack framework for compactifying Picard varieties over ar M_g and characterizes loci with Deligne-Mumford stack structures.

Findings

Constructs algebraic stacks over ar M_g for Picard variety compactification

Identifies loci where these stacks are Deligne-Mumford and strongly representable

Provides a functorial and geometric description of the compactification process

Abstract

We study algebraic (Artin) stacks over $\bar{\mathcal M}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves over which we get Deligne-Mumford stacks strongly representable over $\bar{\mathcal M}_g$.