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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Uniqueness of holomorphic curves into abelian varieties
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by Matthew Dulock and Min Ru PDF
Trans. Amer. Math. Soc. 363 (2011), 131-142 Request permission

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
  • 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.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 131-142
  • MSC (2000): Primary 32H30; Secondary 14K20
  • DOI: https://doi.org/10.1090/S0002-9947-2010-04888-3
  • MathSciNet review: 2719675