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2021 Skeletons of Prym varieties and Brill–Noether theory
Yoav Len, Martin Ulirsch
Algebra Number Theory 15(3): 785-820 (2021). DOI: 10.2140/ant.2021.15.785

Abstract

We show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) to the tropical Prym variety of the associated tropical double cover. This confirms a conjecture by Jensen and the first author. We prove a new upper bound on the dimension of the Prym–Brill–Noether locus for a generic unramified double cover in a dense open subset in the moduli space of unramified double covers of curves with fixed even gonality on the base. Our methods also give a new proof of the classical Prym–Brill–Noether theorem for generic unramified double covers that is originally due to Welters and Bertram.

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Yoav Len. Martin Ulirsch. "Skeletons of Prym varieties and Brill–Noether theory." Algebra Number Theory 15 (3) 785 - 820, 2021. https://doi.org/10.2140/ant.2021.15.785

Information

Received: 7 May 2020; Revised: 27 August 2020; Accepted: 10 October 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.785

Subjects:
Primary: 14H40 , 14Txx

Keywords: folded chain of loops , non-Archimedean uniformization , Prym–Brill–Noether locus , tropical Prym variety

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 3 • 2021
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