一个圆环上全纯映射的Nevanlinna理论第二基本定理
PDF下载 (192)高玉辉,于光升.一个圆环上全纯映射的Nevanlinna理论第二基本定理[J].宁波大学学报(理工版),2024,37(5):41-47.DOI:10.20098/j.cnki.1001-5132.2024.0412
GAO Yuhui,YU Guangsheng.A second main theorem of Nevanlinna theory for holomorphic mappings on annuli[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(5):41-47.DOI:10.20098/j.cnki.1001-5132.2024.0412
| Title: | A second main theorem of Nevanlinna theory for holomorphic mappings on annuli |
| 作者: | 高玉辉, 于光升 |
| Author(s): | GAO Yuhui, YU Guangsheng |
| 关键词: | Nevanlinna理论; 强 -次一般位置; 第二基本定理; Nochka权 |
| Keywords: | Nevanlinna theory; strong -subgeneral position; second main theorem; Nochka weight |
| 分类号: | O174 |
| DOI: | 10.20098/j.cnki.1001-5132.2024.0412 |
| 文献标识码: | A |
| 摘要: | 为了建立圆环上的全纯映射和处于强 -次一般位置的超曲面交的第二基本定理, 采用了Nochka权方法. 首先用Nochka权将关于所有超曲面的Weil函数用部分超曲面的Weil函数控制; 然后将超曲面嵌入到高维射影空间中变成超平面, 并构造线性非退化全纯映射; 进而利用圆环上关于超平面推广的Cartan第二基本定理, 给出圆环上代数非退化全纯映射和超曲面处于强 -次一般位置的第二基本定理. |
| Abstract: | To establish a second main theorem for holomorphic mappings on annuli intersecting hypersurfaces in strong -subgeneral position, the Nochka weight is employed. First, the sum of Weil functions of all hypersurfaces are controlled by the sum of partial hypersurfaces with Nochka weights. Then, the hypersurfaces are embedded into a high-dimensional projective space to be hyperplanes, and a linearly non-degenerate holomorphic mapping is constructed. Finally, a second main theorem is established for algebraically non-degenerate holomorphic mappings on the annuli intersecting hypersurfaces in strong -subgeneral position by the generalized form of Cartan’s second main theorem. |
| 参考文献 /References: | [1] NEVANLINNA R. Zur theorie der meromorphen funktionen[J]. Acta Mathematica, 1925, 46(1/2):1-99. [2] CARTAN H. Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications[J]. Annales Scientifiques de l'École Normale Supérieure, 1928, 45(3):255-346. [3] AHLFORS L. The theory of meromorphic curves[J]. Acta Societatis Scientiarum Fennicae: Nova Series A, 1941, 3(4):171-183. [4] CARLSON J, GRIFFITHS P. A defect relation for equidimensional holomorphic mappings between algebraic varieties[J]. The Annals of Mathematics, 1972, 95(3):577-584. [5] RU M. Holomorphic curves into algebraic varieties[J]. Annals of Mathematics, 2009, 169(1):255-267. [6] BIEBERBACH L. Theorie der gewöhnlichen differentialgleichungen[M]. Berlin: Springer, 1965. [7] PHUONG H T, THIN N V. On fundamental theorems for holomorphic curves on the annuli[J]. Ukrainian Mathematical Journal, 2015, 67(7):1111-1125. [8] PHUONG H T, VILAISAVANH L. On fundamental theorems for holomorphic curves on an annulus intersecting hypersurfaces[J]. Bulletin of the Iranian Mathematical Society, 2022, 48(1):151-163. [9] DETHLOFF G, VAN TAN T, THAI D D. An extension of the cartan-nochka second main theorem for hypersurfaces [J]. International Journal of Mathematics, 2011, 22(6): 863-885. [10] EVERTSE J H, FERRETTI R G. A generalization of the subspace theorem with polynomials of higher degree [C]//SCHLICKEWEI H P, SCHMIDT K, TICHY R F. Diophantine approximation. Vienna: Springer, 2008:175- 198. [11] EVERTSE J H, FERRETTI R G. Diophantine inequalities on projective varieties[J]. International Mathematics Research Notices, 2002, 2002(25):1295-1330. |
| 备注/Memo: | 收稿日期: 2024−04−08. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（12271275）. 第一作者: 高玉辉, 硕士研究生, 主要研究方向: 多复变. E-mail: 2476435354@qq.com *通信作者: 于光升, 博士/副教授, 主要研究方向: 多复变. E-mail: yuguangsheng@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
