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Compactifying the relative Jacobian over families of reduced curves
Author(s):
Eduardo
Esteves
Journal:
Trans. Amer. Math. Soc.
353
(2001),
3045-3095.
MSC (2000):
Primary 14H40, 14H60;
Secondary 14D20
Posted:
January 18, 2001
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Abstract:
We construct natural relative compactifications for the relative Jacobian over a family  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  of simple, torsion-free, rank-1 sheaves on  , and showing that certain open subsheaves of  have the completeness property. Strictly speaking, the functor  is only representable by an algebraic space, but we show that  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
DOI:
10.1090/S0002-9947-01-02746-5
PII:
S 0002-9947(01)02746-5
Received by editor(s):
December 15, 1997
Received by editor(s) in revised form:
May 2, 2000
Posted:
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 of article:
Copyright
2001,
American Mathematical Society
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