Normal Families of Meromorphic Mappings of Several Complex Variables for Moving Hypersurfaces in a Complex Projective Space

TL;DR

This paper establishes new sufficient conditions for the normality of families of meromorphic mappings from complex n-space to projective space, based on their uniform intersection behavior with moving hypersurfaces, extending prior research in the field.

Contribution

It provides generalized and complete criteria for meromorphic normality considering weak intersection conditions with moving hypersurfaces, advancing previous theoretical frameworks.

Findings

Established new criteria for meromorphic normality.

Extended previous results to more general moving hypersurface conditions.

Unified and generalized earlier theorems in the field.

Abstract

The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in P^N(C), namely that their intersections with these moving hypersurfaces, which may moreover depend on the meromorphic maps, are in some sense uniform. Our results generalise and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang and the recent work of Quang-Tan.