English

Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties

Complex Variables 2025-12-11 v1 Algebraic Geometry

Abstract

In 1953, W. Stoll proposed a method of studying holomorphic functions of several complex variables by reducing them to one variable through fiber integration. In this paper, we use this method to extend some important Nevanlinna-type results for holomorphic curves into projective varieties to meromorphic maps from Cp{\Bbb C}^{p} to projective varieties. This includes Bloch's theorem and Noguchi-Winklemann-Yamanoi's Second Main Theorem for holomorphic maps into semi-abelian varieties intersecting an effective divisor, as well as Huynh-Vu-Xie's Second Main Theorem for meromorphic maps into projective space intersecting with a generic hypersurface with sufficiently high degree.

Keywords

Cite

@article{arxiv.2512.09805,
  title  = {Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties},
  author = {Zhe Wang},
  journal= {arXiv preprint arXiv:2512.09805},
  year   = {2025}
}