Meromorphic mappings into projective varieties with arbitrary families of moving hypersurfaces

TL;DR

This paper establishes a comprehensive second main theorem for meromorphic mappings into projective subvarieties with arbitrary moving hypersurfaces, advancing the understanding of value distribution in complex geometry.

Contribution

It generalizes and improves all previous second main theorems for meromorphic mappings with moving hypersurfaces, especially in subgeneral position, using a novel proof method.

Findings

General second main theorem for meromorphic mappings into subvarieties

Extension to arbitrary families of moving hypersurfaces

Improved bounds and conditions compared to previous results

Abstract

In this paper, we prove a general second main theorem for meromorphic mappings into a subvariety $V$ of $\mathbb P^N(\mathbb C)$ with an arbitrary family of moving hypersurfaces. Our second main theorem generalizes and improves all previous results for meromorphic mappings with moving hypersurfaces, in particular for meromorphic mappings and families of moving hypersurfaces in subgeneral position. The method of our proof is different from that of previous authors used for the case of moving hypersurfaces.