Degeneracy second main theorems for meromorphic mappings into projective varieties with hypersurfaces

TL;DR

This paper extends the second main theorem for meromorphic mappings into projective varieties intersecting hypersurfaces, providing explicit truncation levels and improved estimates, generalizing classical results and offering a new proof for projective space cases.

Contribution

It establishes a second main theorem with explicit truncation levels for arbitrary projective varieties, extending classical and recent results, and improves estimates for the projective space case.

Findings

Explicit truncation levels for counting functions are provided.

The theorem generalizes classical results to arbitrary projective varieties.

A new proof with better estimates for projective space is presented.

Abstract

The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of hypersurfaces in subgeneral position. In our result, the truncation level of the counting functions is estimated explicitly. Our result is an extension of the classical second main theorem of H. Cartan, also is a generalization of the recent second main theorem of M. Ru and improves some recent results. The second purpose of this paper is to give another proof for the second main theorem for the special case where the projective variety is a projective space, by which the truncation level of the counting functions is estimated better than that of the general case.