Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The compactified Picard scheme of the compactified Jacobian   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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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph