Compactifications of the universal Jacobian over curves with marked points

Abstract

We construct modular compactifications of the universal Jacobian stack over the moduli stack of reduced curves with marked points depending on stability parameters obtained out of fixing a vector bundle on the universal curve. When restricted to the locus of stable marked curves, 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. We conclude by indicating a number of different possible applications for our constructions.

Exposition improved. Added Application to Universal Néron models for Jacobians of curves with marked points

References in corpus (6)

• Double ramification cycles on the moduli spaces of curves
• Moduli of Singular Curves
• Extensions of the universal theta divisor
• Compactified universal jacobian and the double ramification cycle
• Néron models of $Pi{c}^0$ via $Pi{c}^0$
• Universal Néron models for curves with marked points

Cited by in corpus (5)

• The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian
• Powers of the theta divisor and relations in the tautological ring
• Compactified universal jacobian and the double ramification cycle
• A universal tropical Jacobian over $M_g^{\trop}$
• Universal Néron models for curves with marked points