The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian

Abstract

For each universal genus- g polarization μ of degree d, we construct a universal tropical Jacobian J μ , g t r o p as a generalized cone complex over the moduli space of stable pointed genus- g tropical curves. We show several properties of the space J μ , g t r o p . In particular, we prove that the natural compactification of J μ , g t r o p is the tropicalization of the Esteves' compactified universal Jacobian over the moduli space of stable pointed genus- g curves.