Abstract
We study the tropicalization of the moduli space of algebraic spin curves, \(\overline{\mathcal {S}}_{g,n}\). We exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves \(\overline{S}_{g,n}^{{\text {trop}}}\), prove that is naturally isomorphic to the skeleton of the analytification, \(\overline{S}_{g,n}^{{\text {an}}}\), of \(\overline{\mathcal {S}}_{g,n}\), and give a geometric interpretation of the retraction of \(\overline{S}_{g,n}^{{\text {an}}}\) onto its skeleton in terms of a tropicalization map \(\overline{S}_{g,n}^{{\text {an}}}\rightarrow \overline{S}_{g,n}^{{\text {trop}}}\).
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Acknowledgements
We thank Alex Abreu, Eduardo Esteves, Martin Ulirsch, and Filippo Viviani for several useful remarks. Part of the material in this paper is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the first named author was visiting the Mathematical Sciences Research Institute in Berkeley, California.
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Caporaso, L., Melo, M. & Pacini, M. Tropicalizing the moduli space of spin curves. Sel. Math. New Ser. 26, 16 (2020). https://doi.org/10.1007/s00029-020-0539-y
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DOI: https://doi.org/10.1007/s00029-020-0539-y