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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Compactifying the relative Jacobian over families of reduced curves
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by Eduardo Esteves PDF
Trans. Amer. Math. Soc. 353 (2001), 3045-3095 Request permission

Abstract:

We construct natural relative compactifications for the relative Jacobian over a family $X/S$ of reduced curves. In contrast with all the available compactifications so far, ours admit a Poincaré sheaf after an étale base change. Our method consists of studying the étale sheaf $F$ of simple, torsion-free, rank-1 sheaves on $X/S$, and showing that certain open subsheaves of $F$ have the completeness property. Strictly speaking, the functor $F$ is only representable by an algebraic space, but we show that $F$ is representable by a scheme after an étale base change. Finally, we use theta functions originating from vector bundles to compare our new compactifications with the available ones.
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Additional Information
  • Eduardo Esteves
  • Affiliation: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro RJ, Brazil
  • Email: esteves@impa.br
  • Received by editor(s): December 15, 1997
  • Received by editor(s) in revised form: May 2, 2000
  • Published electronically: January 18, 2001
  • Additional Notes: Research supported by an MIT Japan Program Starr fellowship, by PRONEX, Convênio 41/96/0883/00 and CNPq, Proc. 300004/95-8.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 3045-3095
  • MSC (2000): Primary 14H40, 14H60; Secondary 14D20
  • DOI: https://doi.org/10.1090/S0002-9947-01-02746-5
  • MathSciNet review: 1828599