全纯曲线族涉及导曲线与分担超平面的正规定则

Normal Criteria for Holomorphic Curves Relating to Derived Curves and Shared Hyperplanes

本文基于值分布理论和正规族理论以及高等代数相关知识及研究方法,将复射影空间的全纯曲线族与导曲线相结合,对全纯曲线族分担超平面的正规性进行了研究,得到了N = 4时全纯曲线的正规性。设是从到的一族全纯映射,是上处于一般位置的超平面,其中,。假定对任意的满足条件:当且仅当,;若的并集,则有大于或等于,,是常数,则在D上正规。

This article is based on value distribution theory, normal family theory, and advanced algebra related knowledge and research methods. It combines the family of holomorphic curves in complex projective spaces with derivative curves to study the normality of holomorphic curve families sharing hyperplanes, and obtain the normality of holomorphic curves at N = 4. Let be a family of holomorphic maps of a domain into . Let be hyperplanes in located in general position, where , . Assume the following conditions hold for every : belongs to , if and only if belongs to ,;if belongs to the union set of , then is equal or greater than , where is a constant. Then is normal on D.