Second main theorem and unicity of meromorphic mappings for hypersurfaces of projective varieties in subgeneral position

The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of \C^m into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions. The second is to show a uniqueness theorem for these mappings which share few hypersurfaces without counting multiplicity.Comment: 16 page

Degeneracy and finiteness theorems for meromorphic mappings in several complex variables

In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with multiplicities more than certain values do not need to be counted. We also show that if three meromorphic mappings $f^1,f^2,f^3$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 5)$ share $2n+1$ hyperplanes in general position with truncated multiplicity then the map $f^1\times f^2\times f^3$ is linearly degenerate.Comment: This paper is accepted for publication in Chinese Annals of Mathematics, Series B, Volume 39, No. 5 (2018

Truncated second main theorem for non-Archimedean meromorphic maps with hypersurfaces in projective varieties

Let $\mathbb F$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of $\mathbb P^M(\mathbb F)$. In this paper, we will prove some second main theorems for non-Archimedean meromorphic maps of $\mathbb F^m$ into $V$ intersecting a family of hypersurfaces in $N-$subgeneral position with truncated counting functions.Comment: This paper has been accepted for publication in Journal of Mathematics and Mathematical Science https://science.thanglong.edu.vn/index.php/volc/article/view/9

Nevanlinna theory for holomophic curves from annuli into semi Abelian varieties

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties intersecting with only one divisor is given.Comment: This paper has been accepted for publication in Mathematica Slovac