2025/01/22 by Alexia Corradini, Corradini, Alexia · 1 voice
Mathematics · Physics and Astronomy · #53D37 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.AG #math.SG
paper · pdf · doi:10.48550/arxiv.2501.12850
openalex publication_date 2025/01/22 · arxiv published 2025/01/22 · openalex created_date 2025/10/10 · arxiv updated 2025/11/10 · openalex updated_date 2026/07/28
We introduce an equivalence relation for Lagrangians in a symplectic manifold known as algebraic Lagrangian cobordism, which is meant to mirror algebraic equivalence of cycles. From this we prove a symplectic, mirror-symmetric analogue of the statement \enquotethe Ceresa cycle is non-torsion in the Griffiths group of the Jacobian of a generic genus 3 curve. Namely, we show that for a family of tropical curves, the Lagrangian Ceresa cycle, which is the Lagrangian lift of their tropical Ceresa cycle to the corresponding Lagrangian torus fibration, is non-torsion in its oriented algebraic Lagrangian cobordism group. We proceed by developing the notions of tropical (resp. symplectic) flux, which are morphisms from the tropical Griffiths (resp. algebraic Lagrangian cobordism) groups.