Hyperbolicity of projective hypersurfaces
Author(s)
Bibliographic Information
Hyperbolicity of projective hypersurfaces
(IMPA monographs, v. 5)
Springer, c2016
Available at 10 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
DIV||2||1200035888236
Note
Includes bibliographical references (p. 87-89)
Description and Table of Contents
Description
This
book presents recent advances on Kobayashi hyperbolicity in complex geometry,
especially in connection with projective hypersurfaces. This is a very active
field, not least because of the fascinating relations with complex algebraic
and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta,
among others, resulted in precise conjectures regarding the interplay of these
research fields (e.g. existence of Zariski dense entire curves should
correspond to the (potential) density of rational points).
Perhaps
one of the conjectures which generated most activity in Kobayashi hyperbolicity
theory is the one formed by Kobayashi himself in 1970 which predicts that a
very general projective hypersurface of degree large enough does not contain
any (non-constant) entire curves. Since the seminal work of Green and Griffiths
in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it
became clear that a possible general strategy to attack this problem was to
look at particular algebraic differential equations (jet differentials) that
every entire curve must satisfy. This has led to some several spectacular
results. Describing the state of the art around this conjecture is the main
goal of this work.
Table of Contents
- Introduction.- Kobayashi hyperbolicity: basic theory.- Algebraic hyperbolicity.- Jets spaces.- Hyperbolicity and negativity of the curvature.- Hyperbolicity of generic surfaces in projective 3-space.- Algebraic degeneracy for projective hypersurfaces.
by "Nielsen BookData"