Tropicalization of theta characteristics, double covers, and Prym varieties

• David Jensen ^[1] ; Yoav Len ^[2]
  1. [1] University of Kentucky

     University of Kentucky

     Estados Unidos

     
  2. [2] University of Waterloo

     University of Waterloo

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1391-1410
• Idioma: inglés
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• Resumen

  • We study the behavior of theta characteristics on an algebraic curve under the specialization map to a tropical curve. We show that each effective theta characteristic on the tropical curve is the specialization of 2g−1 even theta characteristics and 2g−1 odd theta characteristics. We then study the relationship between unramified double covers of a tropical curve and its theta characteristics, and use this to define the tropical Prym variety.