本文選題：復射影空間 + 全純映射　； 參考：《華東師范大學》2016年博士論文

【摘要】：本文旨在研究到復射影空間pN(C)的多復變?nèi)冇成浠騺喖冇成涞恼?guī)性和值分布,得到一些新的定理,推廣和改進了已有的結果.首先,在第三章中研究了涉及分擔超曲面的多復變?nèi)冇成湔?guī)族.得到兩個相關正規(guī)定則,其一表明一族全純映射兩兩分擔2t+1個處于t次一般位置的超平面便正規(guī);其二斷言兩族全純映射對應兩兩分擔3t+1個處于t次一般位置的超曲面有相同的正規(guī)性,它們推廣了Montel定則等經(jīng)典結果,舉出例子說明以上是兩種不同的問題.在第四章,首次嘗試推廣關于導函數(shù)的正規(guī)族問題,引入導曲線的概念,將W. Schwick關于亞純函數(shù)與其導數(shù)分擔值的正規(guī)定則推廣至全純映射與其導曲線分擔超平面的情形,回到亞純函數(shù),我們結果也改進了原定理.而在第五章,考察多復變亞純映射族的正規(guī)性.應用第三章中的結論減弱了H.Fujimoto亞純正規(guī)定則中的條件.舉例說明全純曲線族亞純地正規(guī)未必正規(guī),因此提出M-正規(guī)的概念,并討論了三者間的關系.同時得到M-正規(guī)的一些充分條件.在第六章,研究了全純曲線的值分布問題.運用Fermat型函數(shù)方程的相關結果構造例子說明了對C到PNⅣ(C)的全純曲線,H. Cartan的截斷型第二基本定理中的最佳截斷水平是N.然后,研究了一類具體的超曲面,給出一個代數(shù)非退化的全純曲線相交一個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，

本文編號：1930299