Tropical Abel-Jacobi theory

Omid Amini; Daniel Corey; Leonid Monin

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arXiv · 2504.14415

Tropical Abel-Jacobi theory

Omid Amini·Daniel Corey·Leonid Monin

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Abstract

To a compact tropical variety of arbitrary dimension, we associate a collection of intermediate Jacobians defined in terms of tropical homology and tropical monodromy. We then develop an Abel-Jacobi theory in the tropical setting by defining functorial Abel-Jacobi maps. We introduce, in particular, tropical Albanese varieties and formulate obstructions to algebraic equivalence of tropical cycles. In dimension 1, we show that this recovers the existing Abel-Jacobi theory for tropical curves. As an application, we consider the Ceresa class of a tropical curve which is defined as the image of the Ceresa cycle in an appropriate intermediate Jacobian under the Abel-Jacobi map. We give an explicit formula for this class entirely in terms of the combinatorics of the tropical curve.

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Omid Amini, Daniel Corey, Leonid Monin. 2025-04-19. Tropical Abel-Jacobi theory. https://arxiv.org/abs/2504.14415

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