Avoidance Criteria for Normal Holomorphic Curves on Complex Projective Space

TL;DR

This paper develops criteria to determine when families of holomorphic curves in complex projective space avoid certain hypersurfaces or hyperplanes, ensuring their normality under specific geometric conditions.

Contribution

It introduces new avoidance criteria for holomorphic curves avoiding moving hypersurfaces and hyperplanes, extending normality results in complex projective geometry.

Findings

Established avoidance criteria for holomorphic curves avoiding moving hypersurfaces.

Derived normality conditions for families sharing hyperplanes.

Extended classical results to more general geometric configurations.

Abstract

We establish an avoidance criterion for families of holomorphic curves from the unit disk in complex plane to the complex projective space that omit sufficiently many moving hypersurfaces in pointwise general position. Furthermore, we study families of holomorphic curves that share hyperplanes and derive analogous normality conditions in this context.