Defect relation for holomorphic maps from complex discs into projective varieties and hypersurfaces

TL;DR

This paper proves a new second main theorem for holomorphic maps from complex discs into projective varieties, providing bounds on defect sums and generalizing previous results for maps from complex planes.

Contribution

It introduces a second main theorem for maps with finite growth index intersecting hypersurfaces in projective varieties, extending and improving prior theorems.

Findings

Established a second main theorem with bounds on truncated defects.

Generalized previous results to maps with finite growth index.

Improved bounds for holomorphic maps intersecting hypersurfaces.

Abstract

In this paper, we establish a second main theorem for holomorphic maps with finite growth index on complex discs intersecting arbitrary families of hypersurfaces (fixed and moving) in projective varieties, which gives an above bound of the sum of truncated defects. Our result also is generalizes and improves many previous second main theorems for holomorphic maps from $\mathbb C$ intersecting hypersurfaces (moving and fixed) in projective varieties.