Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Geometry
Cover of the book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by Junjiro Noguchi, Jörg Winkelmann, Springer Japan
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Junjiro Noguchi, Jörg Winkelmann ISBN: 9784431545712
Publisher: Springer Japan Publication: December 9, 2013
Imprint: Springer Language: English
Author: Junjiro Noguchi, Jörg Winkelmann
ISBN: 9784431545712
Publisher: Springer Japan
Publication: December 9, 2013
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Japan

Cover of the book Illustrated Anatomical Segmentectomy for Lung Cancer by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Drebrin by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Novel Insights in Agent-based Complex Automated Negotiation by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Firms’ Location Selections and Regional Policy in the Global Economy by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Dynamics of Learning in Neanderthals and Modern Humans Volume 1 by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Translational Research in Muscular Dystrophy by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Transglutaminases by Junjiro Noguchi, Jörg Winkelmann
Cover of the book German Business Management by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Time Series Modeling for Analysis and Control by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Liver Diseases and Hepatic Sinusoidal Cells by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Lumbar Fusion and Stabilization by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Ischemic Blood Flow in the Brain by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Bioactive Lipid Mediators by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Porous Metals with Directional Pores by Junjiro Noguchi, Jörg Winkelmann
Cover of the book Topical Themes in Energy and Resources by Junjiro Noguchi, Jörg Winkelmann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy