The trigonal construction and the second moment of the tropical Prym variety

Fuente: arXiv
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Main Author: Zakharov, Dmitry
Format: Preprint
Published: 2025
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author Zakharov, Dmitry
author_facet Zakharov, Dmitry
contents We use the tropical trigonal construction to calculate the second moment of the tropical Prym variety of all double covers $π:\widetildeΓ\to Γ$ of tropical curves of genus $g(Γ)\leq 4$. The answer is expressed in terms of the signed graphic matroid of the double cover and consists a polynomial and piecewise-polynomial term. We relate the latter term, which does not occur in the analogous formula for the tropical Jacobian, to the problem of extending the Prym--Torelli map from the moduli space of admissible double covers to the second Voronoi compactification of the moduli space of principally polarized abelian varieties.
format Preprint
id arxiv_https___arxiv_org_abs_2507_06401
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The trigonal construction and the second moment of the tropical Prym variety
Zakharov, Dmitry
Algebraic Geometry
Combinatorics
14H40 (primary), 14T20, 05C22
We use the tropical trigonal construction to calculate the second moment of the tropical Prym variety of all double covers $π:\widetildeΓ\to Γ$ of tropical curves of genus $g(Γ)\leq 4$. The answer is expressed in terms of the signed graphic matroid of the double cover and consists a polynomial and piecewise-polynomial term. We relate the latter term, which does not occur in the analogous formula for the tropical Jacobian, to the problem of extending the Prym--Torelli map from the moduli space of admissible double covers to the second Voronoi compactification of the moduli space of principally polarized abelian varieties.
title The trigonal construction and the second moment of the tropical Prym variety
topic Algebraic Geometry
Combinatorics
14H40 (primary), 14T20, 05C22
url https://arxiv.org/abs/2507.06401