Tropicalizing the moduli space of spin curves

• Lucia Caporaso ^[3] ; Margarida Melo ^[1] ; Marco Pacini ^[2]
  1. [1] Universidade de Coimbra

     Universidade de Coimbra

     Coimbra (Sé Nova), Portugal

     
  2. [2] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     
  3. [3] Università Roma Tre, Italia

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-0539-y
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• Resumen

  • 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¯¯¯tropg,n, prove that is naturally isomorphic to the skeleton of the analytification, S¯¯¯ang,n, of S¯¯¯g,n, and give a geometric interpretation of the retraction of S¯¯¯ang,n onto its skeleton in terms of a tropicalization map S¯¯¯ang,n→S¯¯¯tropg,n.