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

   

 

Uniqueness of holomorphic curves into abelian varieties


Authors: Matthew Dulock and Min Ru
Journal: Trans. Amer. Math. Soc. 363 (2011), 131-142
MSC (2000): Primary 32H30; Secondary 14K20
Published electronically: August 24, 2010
MathSciNet review: 2719675
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Abstract: In this paper, we first give a slight improvement of Yamanoi's truncated second main theorem for holomorphic maps into abelian varieties. We then use the result to study the uniqueness problem for such maps. The results obtained generalize and improve E. M. Schmid's uniqueness theorem for holomorphic maps into elliptic curves. In the last section, we consider algebraic dependence for a finite collection of holomorphic curves into an abelian variety.


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Additional Information

Matthew Dulock
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Address at time of publication: Department of Mathematics, University of North Texas, Denton, Texas 76203-5017
Email: dulock11@math.uh.edu

Min Ru
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: minru@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04888-3
Keywords: Abelian variety, uniqueness theorem, holomorphic mappings, algebraic dependency, Nevanlinna theory
Received by editor(s): July 3, 2007
Received by editor(s) in revised form: July 14, 2008
Published electronically: August 24, 2010
Additional Notes: The second author was supported in part by NSA under grant number H98230-09-1-0004.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.