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Remarks to Cartan's Second Main Theorem for holomorphic curves into $ \mathbb{P}^N(\mathbb{C})$


Authors: Liu Yang, Lei Shi and Xuecheng Pang
Journal: Proc. Amer. Math. Soc. 145 (2017), 3437-3445
MSC (2010): Primary 32H30, 32A22, 32H02, 30D05
DOI: https://doi.org/10.1090/proc/13500
Published electronically: April 12, 2017
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Abstract: In 1933, H. Cartan proved a Second Main Theorem for a holomorphic curve into $ \mathbb{P}^N(\mathbb{C})$. Here we give the best possible truncated level in Cartan's result with some examples related to Femart-type equations. In addition, a Second Main Theorem for a holomorphic curve intersecting a fixed hypersurface is also obtained.


References [Enhancements On Off] (What's this?)

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Additional Information

Liu Yang
Affiliation: School of Mathematics and Physics Science and Engineering, Anhui University of Technology, Ma’anshan, 243032, People’s Republic of China
Email: yangliu20062006@126.com

Lei Shi
Affiliation: Department of Mathematics, Guizhou Normal University, Guiyang, 550025, People’s Republic of China
Email: sishimath2012@163.com

Xuecheng Pang
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
Email: xcpang@math.ecnu.edu.cn

DOI: https://doi.org/10.1090/proc/13500
Keywords: The Second Main Theorem, Nevanlinna theory, holomorphic curves, Femart-type equations
Received by editor(s): July 19, 2016
Received by editor(s) in revised form: September 6, 2016
Published electronically: April 12, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society

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