An explicit estimate on multiplicity truncation in the second main theorem for holomorphic curves encountering hypersurfaces in general position in projective space

TL;DR

This paper provides an explicit estimate for the level of truncation in the second main theorem for holomorphic curves intersecting hypersurfaces in projective space, refining previous weak results.

Contribution

It offers a precise quantitative bound on multiplicity truncation in the second main theorem for holomorphic curves in projective space.

Findings

Explicit estimate for truncation level in second main theorem

Improved understanding of multiplicity truncation in value distribution theory

Refinement of weak Cartan-type theorems

Abstract

Yan and Chen proved a weak Cartan-type second main theorem for holomorphic curves meeting hypersurfaces in projective space that included truncated counting functions. Here we give an explicit estimate for the level of truncation.