# Tropicalizing the moduli space of spin curves

## TL;DR

This paper explores the tropicalization of the moduli space of algebraic spin curves, establishing its combinatorial structure, irreducibility of strata, and its relation to Berkovich analytification, providing new insights into tropical geometry.

## Contribution

It introduces the moduli space of tropical spin curves, proves its isomorphism to the skeleton of the Berkovich analytification, and offers a geometric interpretation of the retraction map.

## Key findings

- Stratification of the tropical moduli space is combinatorial and irreducible.
- The moduli space of tropical spin curves is isomorphic to the skeleton of the Berkovich analytification.
- Provides a geometric interpretation of the retraction map in tropical terms.

## Abstract

We study the tropicalization of the moduli space of algebraic spin curves, exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves, prove that it is isomorphic to the skeleton of the Berkovich analytification of the moduli space of algebraic spin curves, and give a geometric interpretation of the retraction map in terms of a tropicalization map.