Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (2 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
On the second main theorem of Nevanlinna theory for singular divisors with $(k, \ell)$-conditions
Pages: 507 – 522
In this paper, we introduce the $(k, \ell)$-condition on divisors by using germ decompositions and a new ramification current as the curvature current of a singular metric. Then we prove Second Main Theorem type results of Nevanlinna theory for divisors satisfying our $(k, \ell)$-condition with a new ramification term which produces an extra Characteristic Function term of a meromorphic map defined by Jacobian minors. Our Main theorem recovers Lang’s result when $\ell = 1$, and covers the general position case when $k = 1$.
ramification current, $(k, \ell)$-condition, Second Main Theorem, differentiably non-degenerate, negative curvature method
2010 Mathematics Subject Classification
32A22, 32B10, 32H30, 32J25
The authors were partially supported by NSFC 11671090 and 11322103.
Received 12 August 2016
Accepted 21 June 2017
Published 8 August 2018