全纯曲线的例外超平面 庆贺杨乐院士八十华诞  

Exceptional Hyperplanes of Holomorphic Curves

作　　者：柴富杰 高宗升[2] 孙道椿[3] CHAI Fujie;GAO Zongsheng;SUN Daochun(School of Financial Mathematics&Statistics,Guangdong University of Finance,Guangzhou 510521,China;School of Mathematics Science,Beihang University,Beijing 100191,China;School of Mathematics,South China Normal University,Guangzhou 510631,China)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521 [2]北京航空航天大学数学科学学院,北京100191 [3]华南师范大学大学数学科学学院,广州510631

出　　处：《数学年刊（A辑）》2021年第3期305-316,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11501127)的资助.

摘　　要：文章讨论了到复射影空间P^(N)(C)的全纯曲线交超平面的问题,借助Vandermonde行列式,构造了一些具有N+1个例外超平面的非线性退化的全纯曲线和具有2N个例外超平面的线性退化的非常映射全纯曲线,说明了Nochka的全纯曲线的第二基本定理是最优的.最后还构造了具有2N个例外值的N值非常数代数体函数.In this paper,the authors investigate holomorphic curves into P^(N)(C)intersecting with hyperplanes.By using Vandermonde determinant,they construct some linearly non-degenerated holomorphic curves with N+1 exceptional hyperplanes and some linearly degenerated non-constant holomorphic curves with 2N exceptional hyperplanes.It is demonstrated that the inequality in Nochka's second main theorem of holomorphic curves is sharp.Moreover,they also construct some N-value non-constant algebroid functions with 2N exceptional values.

关 键 词：全纯曲线 例外超平面 VANDERMONDE行列式 代数体函数 

分 类 号：O174.52[理学—数学] O174.56[理学—基础数学]