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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.