紧黎曼面上代数曲线的第二基本定理

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1585-1597.

• 论文 • 下一篇

紧黎曼面上代数曲线的第二基本定理

段丽珍,曹红哲*()

^{南昌大学理学院数学系南昌 330031}

收稿日期:2020-09-25 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 曹红哲 E-mail:hongzhecao@ncu.edu.cn; 1937018403@qq.com
基金资助:
国家自然科学基金(12061041);国家自然科学基金(12061042)

Second Main Theorem for Algebraic Curves on Compact Riemann Surfaces

Lizhen Duan,Hongzhe Cao*()

^{Department of Mathematics, College of Science, Nanchang University, Nanchang 330031}

Received:2020-09-25 Online:2021-12-26 Published:2021-12-02
Contact: Hongzhe Cao E-mail:hongzhecao@ncu.edu.cn; 1937018403@qq.com
Supported by:
the NSFC(12061041);the NSFC(12061042)

摘要/Abstract

摘要：

该文建立了从紧黎曼曲面到复射影簇上代数曲线关于处于次一般位置超曲面的第二基本定理，得到了从紧黎曼曲面到复射影空间代数曲线涉及更小截断重数的第二基本定理.其次运用第二基本定理证明了射影空间中全曲率有限完备极小曲面的高斯映射的分歧定理.

关键词: 第二基本定理, 极小曲面上的高斯映射, 代数曲线, 超曲面

Abstract:

In this paper, we first establish some second main theorems for algebraic curves from a compact Riemann surface into a complex projective subvariety of the complex projective space, which is ramified over hypersurfaces in subgeneral position. Then we use it to study the ramification for the generalized Gauss map of complete regular minimal surfaces in $\mathbb{R}^{m}$ with finite total curvature.

Key words: Second main theorem, Gauss map of minimal surfaces, Algebraic curves, Hypersurfaces

中图分类号:

O174.5

段丽珍,曹红哲. 紧黎曼面上代数曲线的第二基本定理[J]. 数学物理学报, 2021, 41(6): 1585-1597.

Lizhen Duan,Hongzhe Cao. Second Main Theorem for Algebraic Curves on Compact Riemann Surfaces[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1585-1597.

参考文献

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紧黎曼面上代数曲线的第二基本定理

Second Main Theorem for Algebraic Curves on Compact Riemann Surfaces

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