Tropicalization of theta characteristics, double covers, and Prym varieties
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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.
Jensen , D & Len , Y 2018 , ' Tropicalization of theta characteristics, double covers, and Prym varieties ' , Selecta Mathematica: New Series , vol. 24 , no. 2 , pp. 1391–1410 . https://doi.org/10.1007/s00029-017-0379-6
Selecta Mathematica: New Series
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