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Introduction to Complex Hyperbolic Spaces

Authors: Lang, Serge

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About this book

Since the appearance of Kobayashi's book, there have been several re­ sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re­ produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super­ sede Kobayashi's. My interest in these matters stems from their relations with diophan­ tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan­ linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.

Table of contents (9 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4757-1945-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-387-96447-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-1-4419-3082-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Complex Hyperbolic Spaces
Authors
Copyright
1987
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-1945-1
DOI
10.1007/978-1-4757-1945-1
Hardcover ISBN
978-0-387-96447-8
Softcover ISBN
978-1-4419-3082-8
Edition Number
1
Number of Pages
VIII, 272
Topics