Tropical Donagi theorem

Felix Röhrle; Thomas Saillez

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arXiv · 2507.05987

Tropical Donagi theorem

Felix Röhrle·Thomas Saillez

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Abstract

The tropical $n$-gonal construction was introduced in recent work by the first author and D.~Zakharov and structural results for $n = 2,3$ were established. In this article we explore the construction for $n = 4$ and prove a tropical analogue of Donagi's theorem which states that the tetragonal construction is a triality which preserves Prym varieties. This confirms the speculations in previous work and establishes new results on the non-injectivity of the tropical Prym-Torelli morphism. Finally, we demonstrate that the tropical $n$-gonal construction is poorly behaved under edge contractions, thus preventing any immediate moduli-theoretic perspective.

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Felix Röhrle, Thomas Saillez. 2025-07-08. Tropical Donagi theorem. https://arxiv.org/abs/2507.05987

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