Degeneracy theorems for two holomorphic curves in $ \mathbb{P}^n(\mathbb{C})$ sharing few hypersurfaces

Kai Zhou and Lu Jin

Vol. 302 (2019), No. 1, 371–383

DOI: 10.2140/pjm.2019.302.371

Abstract

In value distribution theory, many uniqueness and degeneracy theorems for holomorphic curves in ${\mathbb{P}}^n\left(ℂ\right)$ sharing hyperplanes or sharing sufficiently many hypersurfaces have been obtained in the last few decades. But there is no result concerning holomorphic curves in ${\mathbb{P}}^n\left(ℂ\right)$ sharing few hypersurfaces. We prove several degeneracy theorems for two algebraically nondegenerate holomorphic curves in ${\mathbb{P}}^n\left(ℂ\right)$ sharing $n+k$ hypersurfaces in general position.

Keywords

degeneracy theorem, hypersurface, holomorphic curve, Nevanlinna theory

Mathematical Subject Classification 2010

Primary: 32H30

Secondary: 30D35

Milestones

Received: 20 January 2019

Accepted: 13 March 2019

Published: 5 November 2019