| 柴富杰,高宗升,孙道椿.全纯曲线的例外超平面∗[J].数学年刊A辑,2021,42(3):305~316 |
| 全纯曲线的例外超平面∗ |
| Exceptional Hyperplanes of Holomorphic Curves |
| Received:May 08, 2019 Revised:November 05, 2019 |
| DOI：10.16205/j.cnki.cama.2021.0024 |
| 中文关键词: 全纯曲线,例外超平面,Vandermonde~行列式,代数体函数 |
| 英文关键词:Holomorphic curves, Exceptional hyperplanes, Vandermonde determinant, Algebroid functions |
| 基金项目:国家自然科学基金 (No.11501127) |
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| 中文摘要: |
| 文章讨论了到复射影空间PN (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. |
| 英文摘要: |
| In this paper, the authors investigate holomorphic curves into PN (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. |
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