An Abel-Jacobi theorem for metrized complexes of Riemann surfaces

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.

19 pages, 3 figures, v2, to appear in Advances in Geometry, comments still very welcome!