If a smooth projective variety $X$ admits a non-degenerate holomorphic map $ℂ\to X$ from the complex plane $ℂ$, then for any finite dimensional linear representation of the fundamental group of $X$ the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

The purpose of this article is twofold. The first is to give necessary conditions for the maximality of the defect sum. The second is to show that the class of meromorphic functions with maximal defect sum is very thin in the sense that deformations of meromorphic functions with maximal defect sum by small meromorphic functions are not meromorphic functions with maximal defect sum.

The purpose of this paper is twofold. The first is to weaken or omit the condition $dim{f}^{-1}\left(H_i\cap H_j\right)\le m-2$ for i ≠ j in some previous uniqueness theorems for meromorphic mappings. The second is to decrease the number q of hyperplanes $H_j$ such that f(z) = g(z) on ${\bigcup }_{j=1}^q{f}^{-1}\left(H_j\right)$, where f,g are meromorphic mappings.