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

 

The second main theorem of holomorphic curves into projective spaces


Authors: Pei-Chu Hu and Chung-Chun Yang
Journal: Trans. Amer. Math. Soc. 363 (2011), 6465-6479
MSC (2010): Primary 32H02, 32H25
Published electronically: July 26, 2011
MathSciNet review: 2833564
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Abstract: By utilizing Jacobian sections introduced by Stoll, we prove a second main theorem of holomorphic curves into projective spaces for hypersurfaces under certain conditions on the jets of the curves. The precise conditions are listed in three equations in the introduction. This solves a weaker form of Griffiths' conjecture and only for a special class of holomorphic curves.


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Additional Information

Pei-Chu Hu
Affiliation: Department of Mathematics, Shandong University, Jinan 250100, Shandong, People’s Republic of China
Email: pchu@sdu.edu.cn

Chung-Chun Yang
Affiliation: Department of Mathematics, The Hong Kong University of Science & Technology, Hong Kong, People’s Republic of China
Email: chungchun.yang@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05394-8
PII: S 0002-9947(2011)05394-8
Keywords: Holomorphic curve, projective space, line bundle, Jacobian section, value distribution theory.
Received by editor(s): September 16, 2007
Received by editor(s) in revised form: December 17, 2009
Published electronically: July 26, 2011
Additional Notes: The work of the first author was partially supported by the Natural Science Foundation of China and Shandong
The second author was partially supported by a UGC Grant of Hong Kong: Project No. 604103.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.