Selecta Mathematica

, Volume 24, Issue 2, pp 1391–1410 | Cite as

Tropicalization of theta characteristics, double covers, and Prym varieties

Article

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.

Mathematics Subject Classification

14T05 14H40 

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Notes

Acknowledgements

The bulk of this paper was written during a Research in Pairs stay at Oberwolfach. We would like to thank the institute for providing ideal working conditions for exploring these ideas. The first author’s travel was supported by an AMS Simons travel grant, and the second author was partially support by DFG Grant MA 4797/6-1. We are grateful to Matt Baker for insightful remarks on a previous version of this manuscript, and thank Sam Payne, Joe Rabinoff, Dhruv Ranganathan, and Farbod Shokrieh for fielding our questions. Finally, we thank the referees for their insightful remarks.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of KentuckyLexingtonUSA
  2. 2.University of WaterlooWaterlooCanada

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