The compactified Picard scheme of the compactified Jacobian |
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Authors: | Eduardo Esteves Steven Kleiman |
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Institution: | a Instituto de Matemática Pura e Aplicada, Estrada D. Castorina 110, 22460-320 Rio de Janeiro RJ, Brazil b Department of Mathematics, Room 2-278 MIT, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA |
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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 corresponding Abel map , which maps C into its compactified Jacobian, and form its pullback map , which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, double points, then is known to be an isomorphism. We prove that always extends to a map between the natural compactifications, , and that the extended map is an isomorphism if C has, at worst, ordinary nodes and cusps. |
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Keywords: | Primary 14H40 secondary 14K30 14H20 |
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