Abstract
We study a compactification of the moduli space of theta characteristics, giving a modular interpretation of the geometric points and describing the boundary stratification. This space is different from the moduli space of spin curves. The modular description and the boundary stratification of the new compactification are encoded by a tropical moduli space. We show that this tropical moduli space is a refinement of the moduli space of spin tropical curves. We describe explicitly the induced decomposition of its cones.
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Acknowledgements
This is a part of the Ph.D. thesis of the third author supervised by the first and second author. We thank Ethan Cotterill and Margarida Melo for some discussions and for the positive comments on a preliminary version of the paper. We also thank the anonymous referee for helpful suggestions.
Funding
Marco Pacini was supported by CNPq-PQ, 301671/2019-2. Danny Taboada was supported by Capes.
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Abreu, A., Pacini, M. & Taboada, D. The moduli space of quasistable spin curves. Collect. Math. 75, 27–80 (2024). https://doi.org/10.1007/s13348-022-00377-2
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DOI: https://doi.org/10.1007/s13348-022-00377-2