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Skeletons of Prym
varieties and Brill–Noether theory
Yoav Len and Martin Ulirsch |
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Vol. 15 (2021), No. 3, 785–820
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Abstract |
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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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Keywords
tropical Prym variety, non-Archimedean uniformization,
folded chain of loops, Prym–Brill–Noether locus
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Mathematical Subject Classification
Primary: 14H40, 14Txx
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Milestones
Received: 7 May 2020
Revised: 27 August 2020
Accepted: 10 October 2020
Published: 20 May 2021
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Authors |
| Yoav Len | |
| Mathematical Institute University of St. Andrews St. Andrews United Kingdom |
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| Martin Ulirsch | |
| Institut für Mathematik Goethe-Universität Frankfurt Frankfurt am Main Germany |
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