Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

種類:

電子ブック

責任表示:

by Junjiro Noguchi, Jörg Winkelmann

出版情報:

Tokyo : Springer Japan : Imprint: Springer, 2014

著者名:

• Noguchi, Junjiro
• Winkelmann, Jörg
• SpringerLink (Online service)

シリーズ名:

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 350

ISBN:

9784431545712 [4431545719]    

注記:

The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-

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