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

TL;DR

This paper establishes a second main theorem and a uniqueness theorem for meromorphic mappings from complex Euclidean spaces into projective varieties, focusing on hypersurfaces in subgeneral position with truncated counting functions.

Contribution

It introduces new second main theorem and unicity results for meromorphic mappings intersecting hypersurfaces in subgeneral position, extending previous value distribution theory.

Findings

Proved a second main theorem for meromorphic mappings with truncated counting functions.

Established a unicity theorem for mappings sharing few hypersurfaces without multiplicity.

Extended value distribution theory to complex projective varieties in subgeneral position.

Abstract

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.