Enriched spin curves on stable curves with two components

TL;DR

This paper introduces enriched spin curves on stable curves with two components, constructing a parameter space via blow-up techniques that extends the moduli space of spin curves, building on Maino’s work on enriched stable curves.

Contribution

It extends Maino’s construction by defining enriched spin curves and establishing their moduli space through blow-up methods.

Findings

Constructed a moduli space for enriched spin curves.

Connected enriched spin curves to blow-ups of the spin curves moduli space.

Extended the framework of enriched stable curves to include spin structures.

Abstract

L. Maino constructed a moduli space for enriched stable curves, by blowing-up the moduli space of Deligne-Mumford stable curves. We introduce enriched spin curves, showing that a parameter space for these objects is obtained by blowing-up the moduli space of spin curves.