# On Nevanlinna - Cartan theory for holomorphic curves with Tsuji characteristics

## TL;DR

This paper extends Nevanlinna-Cartan theory to holomorphic curves on angular domains, establishing fundamental theorems and addressing the uniqueness problem via inverse images of hypersurfaces, with new results in this specific setting.

## Contribution

It introduces the first known results on the uniqueness of holomorphic curves by inverse images of hypersurfaces on angular domains, expanding classical value distribution theory.

## Key findings

- Proves fundamental theorems for holomorphic curves intersecting hypersurfaces on angular domains.
- Establishes a new uniqueness theorem for holomorphic curves in an angle.
- Improves existing results on uniqueness of holomorphic curves on the complex plane.

## Abstract

In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex projective variety with the level of truncation. As applications of the second main theorems for an angle, we will discuss the uniqueness problem of holomorphic curves in an angle instead of the whole complex plane. Detail, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface. In my knowledge, this is the first result for uniqueness problem of holomorphic curve by inverse image of hypersurface on angular domain. On complex plane, we obtain a uniqueness result for holomorphic curves, it is improvement of some results before [5, 10] in this trend.