Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation
Author :
Publisher : Springer Science & Business Media
Total Pages : 425
Release :
ISBN-10 : 9784431545712
ISBN-13 : 4431545719
Rating : 4/5 (12 Downloads)

Book Synopsis Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by : Junjiro Noguchi

Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.


Nevanlinna Theory in Several Complex Variables and Diophantine Approximation Related Books

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation
Language: en
Pages: 425
Authors: Junjiro Noguchi
Categories: Mathematics
Type: BOOK - Published: 2013-12-09 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for g
Nevanlinna Theory in Several Complex Variables and Diophantine Approximation
Language: en
Pages: 432
Authors: Junjiro Noguchi
Categories:
Type: BOOK - Published: 2013-12-31 - Publisher:

DOWNLOAD EBOOK

Several Complex Variables
Language: en
Pages: 582
Authors: Michael Schneider
Categories: Mathematics
Type: BOOK - Published: 1999 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published i
Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition)
Language: en
Pages: 443
Authors: Min Ru
Categories: Mathematics
Type: BOOK - Published: 2021-03-10 - Publisher: World Scientific

DOWNLOAD EBOOK

This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas:
Nevanlinna Theory And Its Relation To Diophantine Approximation
Language: en
Pages: 338
Authors: Min Ru
Categories: Mathematics
Type: BOOK - Published: 2001-06-06 - Publisher: World Scientific

DOWNLOAD EBOOK

It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections. This book provides an introduction t