I will start by reviewing how to compactify the universal Jacobian stack, parametrizing pointed curves endowed with a line bundle, over the moduli stack of stable pointed curves. Then I will discuss logarithmic universal Jacobians and their tropicalization morphism towards the corresponding tropical universal Jacobians. Finally, I will discuss the connection with the Molcho-Wise’s logarithmic Picard and tropical Picard stacks.
This is a joint work with M. Melo, S. Molcho, M. Ulirsch, J. Wise.