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 $J_{\mu ,g}^{trop}$ as a generalized cone complex over the moduli space of stable pointed genus-$g$ tropical curves. We show several properties of the space $J_{\mu ,g}^{trop}$. In particular, we prove that the natural compactification of $J_{\mu ,g}^{trop}$ is the tropicalization of the Esteves' compactified universal Jacobian over the moduli space of stable pointed genus-$g$ curves.

43 pages, 4 figures. Final version. To appear in PLMS. arXiv admin note: text overlap with arXiv:1903.08569