Applications of Kobayashi Hyperbolicity (Chapter 4)

1995 ◽  
pp. 17-21
Keyword(s):  
Kobayashi Hyperbolicity

scholarly journals Algebraically hyperbolic manifolds have finite automorphism groups

2019 ◽  
Vol 22 (02) ◽  
pp. 1950003
Author(s):  
Fedor A. Bogomolov ◽  
Ljudmila Kamenova ◽  
Misha Verbitsky
Keyword(s):  
Positive Constant ◽  
Classical Result ◽  
Automorphism Groups ◽  
Hyperbolic Manifolds ◽  
Projective Manifold ◽  
Kobayashi Hyperbolicity ◽  
Genus Formula ◽  
Projective Manifolds

A projective manifold [Formula: see text] is algebraically hyperbolic if there exists a positive constant [Formula: see text] such that the degree of any curve of genus [Formula: see text] on [Formula: see text] is bounded from above by [Formula: see text]. A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.

Remarks on quasi-Reinhardt domains

2018 ◽  
Vol 149 (2) ◽  
pp. 297-304
Author(s):  
Fengbai Li ◽  
Feng Rong
Keyword(s):  
Reinhardt Domains ◽  
Kobayashi Hyperbolicity ◽  
Fundamental Properties ◽  
Holomorphic Correspondences

AbstractWe present some fundamental properties of quasi-Reinhardt domains, in connection with Kobayashi hyperbolicity, minimal domains and representative domains. We also study proper holomorphic correspondences between quasi-Reinhardt domains.

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