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arXiv · 2507.06401

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

Dmitry Zakharov
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Abstract

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.

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Dmitry Zakharov. 2025-07-08. The trigonal construction and the second moment of the tropical Prym variety. https://arxiv.org/abs/2507.06401

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