In this paper we describe compactifications of the universal Jacobian stack of line bundles over smooth curves obtained by considering open substacks of the moduli stack of torsion-free rank-1 simple sheaves on reduced curves of given genus. The results we describe are mostly expository and based on Altman-Kleiman and Esteves constructions of compactified Jacobians for families of reduced curves. For the moduli stack of Deligne-Mumford n-pointed stable curves, we study fine compactifications obtained by imposing stability conditions on the sheaves and we prove that in this situation we get Deligne-Mumford stacks endowed with a projective coarse moduli space.

Melo, M. (2019). Universal compactified jacobians. PORTUGALIAE MATHEMATICA, 76(2), 101-122 [10.4171/PM/2028].

Universal compactified jacobians

Melo M.
2019-01-01

Abstract

In this paper we describe compactifications of the universal Jacobian stack of line bundles over smooth curves obtained by considering open substacks of the moduli stack of torsion-free rank-1 simple sheaves on reduced curves of given genus. The results we describe are mostly expository and based on Altman-Kleiman and Esteves constructions of compactified Jacobians for families of reduced curves. For the moduli stack of Deligne-Mumford n-pointed stable curves, we study fine compactifications obtained by imposing stability conditions on the sheaves and we prove that in this situation we get Deligne-Mumford stacks endowed with a projective coarse moduli space.
2019
Melo, M. (2019). Universal compactified jacobians. PORTUGALIAE MATHEMATICA, 76(2), 101-122 [10.4171/PM/2028].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/363553
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