Tropicalization of theta characteristics, double covers, and Prym varieties

David Jensen; Yoav Len

doi:10.1007/s00029-017-0379-6

Tropicalization of theta characteristics, double covers, and Prym varieties

David Jensen, Yoav Len

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	1391-1410
Number of pages	20
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s00029-017-0379-6
State	Published - Apr 1 2018

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

Keywords

14H40
14T05

ASJC Scopus subject areas

Mathematics (all)
Physics and Astronomy (all)

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10.1007/s00029-017-0379-6

Cite this

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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.",

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Tropicalization of theta characteristics, double covers, and Prym varieties

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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