Methods and Applications of Analysis

Volume 21 (2014)

Number 4

Special issue dedicated to the 60th birthday of Stephen S.-T. Yau: Part II

Guest editors: John Erik Fornæss, Xiaojun Huang, Song-Ying Li, Yat Sun Poon, Wing Shing Wong, and Zhouping Xin

Some generalizations of the second main theorem intersecting hypersurfaces

Pages: 503 – 526

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n4.a6

Author

Min Ru (Department of Mathematics, University of Houston, Texas, U.S.A.)

Abstract

In Holomorphic curves into algebraic varieties, Annals of Mathematics, 169 (2009), the author established a defect relation for holomorphic mappings from $\mathbb{C}$ into the projective variety $X \subset \mathbb{P}^N (\mathbb{C})$ intersecting divisors of $X$ coming from hypersurfaces in $\mathbb{P}^N$. The purpose of this paper is to do some further generalizations. It contains two major parts: (I) We extend the defect relation to effective divisors on $X$ with $\mathit{Pic}(X) = \mathbb{Z}$. (II) We extend the defect relation to meromorphic mappings from parabolic manifolds into $ X \subset \mathbb{P}^N $.

Keywords

Second Main Theorem, Nevanlinna theory, meromorphic mappings, parabolic manifolds

2010 Mathematics Subject Classification

32H30

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