## Nagoya Mathematical Journal

### Algebraic dependence of meromorphic mappings in value distribution theory

Yoshihiro Aihara

#### Abstract

In this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space $X$ over the complex $m$-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of $X$. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve $E$ and give conditions under which two holomorphic mappings from $X$ into $E$ are algebraically related.

#### Article information

Source
Nagoya Math. J., Volume 169 (2003), 145-178.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631812

Mathematical Reviews number (MathSciNet)
MR1962526

Zentralblatt MATH identifier
1052.32011

#### Citation

Aihara, Yoshihiro. Algebraic dependence of meromorphic mappings in value distribution theory. Nagoya Math. J. 169 (2003), 145--178. https://projecteuclid.org/euclid.nmj/1114631812

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