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

Abstract: For each universal genus-$g$ polarization $\mu$ of degree $d$, we construct a universal tropical Jacobian $J_{\mu,g}<sup>{trop}$ as a generalized cone complex over the moduli space of stable pointed genus-$g$ tropical curves. We show several properties of the space $J_{\mu,g}<sup>{trop}$. In particular, we prove that the natural compactification of $J_{\mu,g}<sup>{trop}$ is the tropicalization of the Esteves' compactified universal Jacobian over the moduli space of stable pointed genus-$g$ curves.