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Uniqueness of holomorphic curves into abelian varieties
Author(s):
Matthew
Dulock;
Min
Ru
Journal:
Trans. Amer. Math. Soc.
363
(2011),
131-142.
MSC (2000):
Primary 32H30;
Secondary 14K20
Posted:
August 24, 2010
MathSciNet review:
2719675
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References |
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Additional information
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.
References:
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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:
10.1090/S0002-9947-2010-04888-3
PII:
S 0002-9947(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
Posted:
August 24, 2010
Additional Notes:
The second author was supported in part by NSA under grant number H98230-09-1-0004.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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