| Résume | The universal Jacobian forms a family of abelian varieties over the moduli space of Deligne--Mumford stable curves of compact type. However, any extension of the universal Jacobian to the full moduli space of stable curves necessarily sacrifices the smoothness or the properness (and also the group structure). However, these properties can be salvaged if one works in an enlarged category of logarithmic schemes (due to Fontaine, Illusie, and Kato). I will describe this logarithmic Picard group and its relationship to other approaches to compactification that operate within the category of schemes. |
