The compactified Picard scheme of the compactified Jacobian

Eduardo Esteves; Steven Kleiman

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The compactified Picard scheme of the compactified Jacobian

Eduardo Esteves·Steven Kleiman

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Abstract

Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the associated Abel map A_L : C -> P, which maps C into its compactified Jacobian scheme P, and form its pullback map A_L^* : Pic^0_P -> J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, double points, then A_L^* is known to be an isomorphism. We prove that A_L^* always extends to a map between the natural compactifications, Pic^-_P -> P, and that the extended map is an isomorphism if C has, at worst, ordinary nodes and cusps.

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Eduardo Esteves, Steven Kleiman. 2004-10-25. The compactified Picard scheme of the compactified Jacobian. https://arxiv.org/abs/math/0410537

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