Tropicalizing the moduli space of spin curves

We study the tropicalization of the moduli space of algebraic spin curves, S¯ g,n. We exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves S¯g,ntrop, prove that is naturally isomorphic to the skeleton of the analytification, S¯g,nan, of S¯ g,n, and give a geometric interpretation of the retraction of S¯g,nan onto its skeleton in terms of a tropicalization map S¯g,nan→S¯g,ntrop