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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Compactifications of the generalized Jacobian variety


Authors: Tadao Oda and C. S. Seshadri
Journal: Trans. Amer. Math. Soc. 253 (1979), 1-90
MSC: Primary 14K30; Secondary 14D25
MathSciNet review: 536936
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Abstract: The generalized Jacobian variety of an algebraic curve with at most ordinary double points is an extension of an abelian variety by an algebraic torus. Using the geometric invariant theory, we systematically compactify it in finitely many different ways and describe their structure in terms of torus embeddings. Our compactifications include all known good ones.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0536936-4
PII: S 0002-9947(1979)0536936-4
Keywords: Generalized Jacobian variety, line bundles, Picard scheme, stable curve, geometric invariant theory, torus embedding, Néron model, Delony decomposition, Voronoi decomposition, Namikawa decomposition, arrangement of hyperplanes, spanning tree, complexity of a graph, Kirchhoff-Trent's theorem, elementary cycle, elementary cocycle
Article copyright: © Copyright 1979 American Mathematical Society