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 | References | Similar Articles | 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.

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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:
https://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.