An Abel-Jacobi theorem for metrized complexes of Riemann surfaces

TL;DR

This paper extends the classical Abel-Jacobi theorem to metrized complexes of Riemann surfaces, bridging complex algebraic geometry and tropical geometry in the context of hybrid spaces.

Contribution

It introduces a new Abel-Jacobi theorem for metrized complexes, unifying classical and tropical cases in a broader geometric framework.

Findings

Established an Abel-Jacobi isomorphism for metrized complexes

Unified classical and tropical Abel-Jacobi theorems

Provided new tools for hybrid space geometry

Abstract

Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel-Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classical Abel-Jacobi theorem and its tropical analogue.