Tropicalization of theta characteristics, double covers, and Prym varieties

Abstract

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 $2^{g-1}$ even theta characteristics and $2^{g-1}$ 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.

20 pages, 7 figures

References in corpus (2)

• Bitangents of tropical plane quartic curves
• Tritangent planes to space sextics: the algebraic and tropical stories

Cited by in corpus (6)

• Skeletons of Prym varieties and Brill--Noether theory
• Kirchhoff's theorem for Prym varieties
• Combinatorics and real lifts of bitangents to tropical quartic curves
• Prym-Brill-Noether Loci of special curves
• Bitangents to plane quartics via tropical geometry: rationality, ${\mathbb{A}}^1$-enumeration, and real signed count
• Avoidance loci and tropicalizations of real bitangents to plane quartics