English

Normal Families of Meromorphic Mappings of Several Complex Variables for Moving Hypersurfaces in a Complex Projective Space

Complex Variables 2015-05-11 v2

Abstract

The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in P^N(C), namely that their intersections with these moving hypersurfaces, which may moreover depend on the meromorphic maps, are in some sense uniform. Our results generalise and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang and the recent work of Quang-Tan.

Keywords

Cite

@article{arxiv.1301.0687,
  title  = {Normal Families of Meromorphic Mappings of Several Complex Variables for Moving Hypersurfaces in a Complex Projective Space},
  author = {Gerd Dethloff and Thai Do Duc and Trang Pham Nguyen Thu},
  journal= {arXiv preprint arXiv:1301.0687},
  year   = {2015}
}

Comments

Final version, to appear in Nagoya Math. J.. Lemma on Hausdorff measure added, and a bit more details are given in the proof of Theorems 1.1 and 1.2