Compactifications of the universal Jacobian over curves with marked points

Margarida Melo

Published 2015-09-21Version 1

We construct modular compactifications of the universal Jacobian stack over the moduli stack of curves with marked points depending on stability parameters obtained out of fixing a vector bundle on the universal curve. Our compactifications are Deligne-Mumford irreducible smooth stacks endowed with projective moduli spaces and, following Esteves approach to the construction of fine compactifications of Jacobians, they parametrize torsion-free rank-1 simple sheaves satisfying a stability condition with respect to the fixed vector bundle. We also study a number of properties of our compactifications as the existence of forgetful and clutching morphisms and as well of sections from the moduli stack of stable curves with marked points; indicating how these could be used in a number of different applications. We also consider compactifications of the universal Jacobian stack over the whole stack of reduced curves.