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

13 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

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

Keywords

14H40
14T05

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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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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AB - 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

Access to Document

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