#### Vol. 302, No. 1, 2019

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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
##### Abstract

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

##### Keywords
degeneracy theorem, hypersurface, holomorphic curve, Nevanlinna theory
Primary: 32H30
Secondary: 30D35