到复射影空间的全纯映射及亚纯映射的正规性和值分布

发布时间：2018-05-24 19:40

  本文选题：复射影空间 + 全纯映射　； 参考：《华东师范大学》2016年博士论文

【摘要】：本文旨在研究到复射影空间pN(C)的多复变全纯映射或亚纯映射的正规性和值分布,得到一些新的定理,推广和改进了已有的结果.首先,在第三章中研究了涉及分担超曲面的多复变全纯映射正规族.得到两个相关正规定则,其一表明一族全纯映射两两分担2t+1个处于t次一般位置的超平面便正规;其二断言两族全纯映射对应两两分担3t+1个处于t次一般位置的超曲面有相同的正规性,它们推广了Montel定则等经典结果,举出例子说明以上是两种不同的问题.在第四章,首次尝试推广关于导函数的正规族问题,引入导曲线的概念,将W. Schwick关于亚纯函数与其导数分担值的正规定则推广至全纯映射与其导曲线分担超平面的情形,回到亚纯函数,我们结果也改进了原定理.而在第五章,考察多复变亚纯映射族的正规性.应用第三章中的结论减弱了H.Fujimoto亚纯正规定则中的条件.举例说明全纯曲线族亚纯地正规未必正规,因此提出M-正规的概念,并讨论了三者间的关系.同时得到M-正规的一些充分条件.在第六章,研究了全纯曲线的值分布问题.运用Fermat型函数方程的相关结果构造例子说明了对C到PNⅣ(C)的全纯曲线,H. Cartan的截断型第二基本定理中的最佳截断水平是N.然后,研究了一类具体的超曲面,给出一个代数非退化的全纯曲线相交一个超曲面的第二基本定理.
[Abstract]:The purpose of this paper is to study the normality and value distribution of multicomplex complex Holomorphic mappings or meromorphic mappings in complex projective space pNX, and obtain some new theorems, which generalize and improve the existing results. Firstly, in chapter 3, we study the normal family of holomorphic mappings with multiple complex variables involving shared hypersurfaces. Two correlated normal rules are obtained. One is that a family of Holomorphic mappings share 2t and 1 hyperplane in the general position of t. Secondly, it is asserted that two classes of Holomorphic mappings share the same normality for pairwise 3t and 1 hypersurface in the general position of degree t. They generalize the classical results such as Montel's rule, and give examples to illustrate the above two different problems. In chapter 4, we first try to generalize the normal family problem about derivative function, introduce the concept of derivative curve, and extend the normal rule of W. Schwick on meromorphic function and its derivative to the case of Holomorphic mapping and its derivative sharing hyperplane. Back to meromorphic functions, our results also improve the original theorem. In the fifth chapter, we investigate the normality of meromorphic mapping families with multiple complex variables. The application of the conclusions in Chapter 3 weakens the conditions in the H.Fujimoto 's orthodox rule. An example is given to show that the family of Holomorphic curves is not normally normal, so the concept of M-normality is proposed and the relations among them are discussed. At the same time, some sufficient conditions of M-normal are obtained. In chapter 6, the value distribution of holomorphic curves is studied. An example of constructing the Fermat type function equation is given to show that the best truncation level in the second fundamental theorem of truncation type of H. Cartan for the Holomorphic curve from C to PN 鈪，

本文编号：1930299