2019/12/18 by Alex Abreu, Sally Andria, Abreu, Alex +5
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1912.08675
openalex publication_date 2019/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study polystable divisors on a tropical curve, which are the tropical analogue of polystable torsion-free rank-1 sheaves on a nodal curve. We construct a universal tropical Jacobian over the moduli space of tropical curves of genus g. This space parametrizes equivalence classes of tropical curves of genus g together with a μ-polystable divisor, and can be seen as a tropical counterpart of Caporaso universal Picard scheme. We describe polyhedral decompositions of the Jacobian of a tropical curve via polystable divisors, relating them with other known polyhedral decompositions.