On the Picard group scheme of the moduli stack of stable pointed curves

TL;DR

This paper investigates the structure of the Picard group and Picard group scheme of the moduli stack of stable pointed curves, providing explicit computations over various base schemes and fields.

Contribution

It offers new insights into the Picard group scheme of the moduli stack and computes Picard groups over fields with characteristic not equal to two.

Findings

Computed Picard groups of the moduli stack over arbitrary schemes.

Determined Picard group scheme structure for the moduli stack.

Provided explicit Picard group calculations over fields of characteristic not two.

Abstract

The aim of the present paper is to study the (abstract) Picard group and the Picard group scheme of the moduli stack of stable pointed curves over an arbitrary scheme. As a byproduct, we compute the Picard groups of the moduli stack of stable or smooth pointed curves over a field of characteristic different from two.