A non-integrated defect relation for holomorphic maps into algebraic varieties

TL;DR

This paper extends the concept of non-integrated defect, originally for maps into projective space, to holomorphic maps into algebraic varieties, providing new value distribution results.

Contribution

It generalizes the non-integrated defect relation from projective space to arbitrary algebraic varieties for holomorphic maps.

Findings

Established non-integrated defect relation for holomorphic maps into algebraic varieties

Generalized Fujimoto's results from projective space to algebraic varieties

Provided new tools for value distribution theory in complex geometry

Abstract

In 1983, relating to the study of value distribution of the Guass maps of complete minimal surfaces in ${\Bbb R}^m$, H. Fujimoto introduced the notion of the non-integrated defect for holomorphic maps of an open Riemann surface into $\mathbb{P}^n(\mathbb{C})$ and obtained some results analogous to the Nevanlinna-Cartan defect relation. This paper establishes the non-integrated defect relation for holomorphic maps into projective varieties.