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Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 455–470 | Cite as

Second Main Theorem and Unicity of Meromorphic Mappings for Hypersurfaces in Projective Varieties

  • Si Duc Quang
  • Do Phuong An
Article

Abstract

Let V be a projective subvariety of \(\mathbb P^{n}(\mathbb C)\). A family of hypersurfaces \(\{Q_{i}\}_{i=1}^{q}\) in \(\mathbb P^{n}(\mathbb C)\) is said to be in N-subgeneral position with respect to V if for any 1≤i 1<⋯<i N+1q, \( V\cap (\bigcap _{j=1}^{N+1}Q_{i_{j}})=\varnothing \). In this paper, we will prove a second main theorem for meromorphic mappings of \(\mathbb C^{m}\) into V intersecting hypersurfaces in subgeneral position with truncated counting functions. As an application of the above theorem, we give a uniqueness theorem for meromorphic mappings of \(\mathbb C^{m}\) into V sharing a few hypersurfaces without counting multiplicity. In particular, we extend the uniqueness theorem for linearly nondegenerate meromorphic mappings of \(\mathbb C^{m}\) into \(\mathbb P^{n}(\mathbb C)\) sharing 2n+3 hyperplanes in general position to the case where the mappings may be linearly degenerated.

Keywords

Holomorphic curves Algebraic degeneracy Defect relation Nochka weight 

Mathematics Subject Classification (2010)

Primary 32H30 Secondary 32H04 32H25 14J70 

Notes

Acknowledgments

This work was completed while the first author was staying at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the Institute for the support.

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2015.03.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam
  2. 2.Division of MathematicsBanking AcademyHanoiVietnam

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