2025/04/19 by Amini, Omid, Corey, Daniel, Monin, Leonid
#05E14 #14C25 #14H40 #14T20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary: 14T10 #Secondary: 05C25
paper · doi:10.48550/arxiv.2504.14415
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.