On the rational Picard group of the moduli space of higher spin curves

TL;DR

This paper refines the definition of higher spin curves by incorporating coherent nets of roots, and describes the boundary of their moduli space along with its rational Picard group.

Contribution

It introduces a refined notion of higher spin curves using torsion-free sheaves and provides a presentation of the rational Picard group of their moduli space.

Findings

Refined the notion of higher spin curves with coherent nets of roots.

Described the boundary of the moduli space of higher spin curves.

Presented the rational Picard group of the moduli space.

Abstract

We refine the notion of higher spin curves defined in terms of line bundles by Caporaso, Cornalba and Casagrande by adding the data of coherent nets of roots introduced by Jarvis in terms of torsion-free sheaves and we describe the boundary part of their moduli space. We provide then a presentation of the rational Picard group of this moduli space.