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Transactions of the American Mathematical Society

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Degeneracy second main theorems for meromorphic mappings into projective varieties with hypersurfaces


Author: Si Duc Quang
Journal: Trans. Amer. Math. Soc. 371 (2019), 2431-2453
MSC (2010): Primary 32H30, 32A22; Secondary 30D35
DOI: https://doi.org/10.1090/tran/7433
Published electronically: October 23, 2018
MathSciNet review: 3896085
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Abstract: The purpose of this paper is twofold. The first purpose is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of hypersurfaces in subgeneral position. In our result, the truncation level of the counting functions is estimated explicitly. Our result is an extension of the classical second main theorem of H. Cartan and is also a generalization of the recent second main theorem of M. Ru and improves some recent results. The second purpose of this paper is to give another proof for the second main theorem for the special case where the projective variety is a projective space, by which the truncation level of the counting functions is estimated better than that of the general case.


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Additional Information

Si Duc Quang
Affiliation: Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam
Address at time of publication: Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam
Email: quangsd@hnue.edu.vn

DOI: https://doi.org/10.1090/tran/7433
Keywords: Nevanlinna theory, second main theorem, meromorphic mappings, hypersurface, subgeneral position
Received by editor(s): August 11, 2017
Published electronically: October 23, 2018
Additional Notes: This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2015.03.
Article copyright: © Copyright 2018 American Mathematical Society