Holomorphic maps from complex discs intersecting families of hypersurfaces

TL;DR

This paper extends second main theorems for holomorphic maps from complex discs to projective varieties, providing detailed estimates for intersections with families of hypersurfaces, generalizing previous results from maps from  to .

Contribution

It introduces new second main theorems for holomorphic maps with finite growth index intersecting hypersurfaces in projective varieties, broadening the scope of prior work.

Findings

Generalized second main theorems for complex disc maps

Detailed estimates for intersection cases

Extended previous results to broader hypersurface families

Abstract

In this paper, we establish second main theorems for holomorphic maps with finite growth index on complex discs intersecting families of hypersurfaces (moving and fixed) in projective varieties, where the small term is detailed estimate for various cases. Our results are generalizations and extensions of many previous second main theorems for holomorphic maps from $\mathbb C$ intersecting with hypersurfaces (moving and fixed) or moving hyperplanes.