Some problems in hyperbolic complex analysis. (English) Zbl 0795.32010
Komatsu, Gen (ed.) et al., Complex geometry. Proceedings of the Osaka international conference, held in Osaka, Japan, Dec. 13-18, 1990. New York: Marcel Dekker. Lect. Notes Pure Appl. Math. 143, 113-120 (1993).
The author states some open problems in hyperbolic complex analysis, and gives for them some background material and motivation. The main problems are the following:
(1) If a projective algebraic manifold is hyperbolic, is it of general type?
(2) If \(X\) is a compact measure hyperbolic space, is \(\operatorname{Aut} (X)\) finite?
(3) If \(Y\) is a compact hyperbolic complex space and \(X\) is an arbitrary compact complex space, is the set of surjective meromorphic maps \(f:X \to Y\) finite?
(4) If an algebraic manifold admits a Hermitian metric (or even a Kähler metric) with negative holomorphic sectional curvature, it is of general type?
For the entire collection see [Zbl 0771.00034].
(1) If a projective algebraic manifold is hyperbolic, is it of general type?
(2) If \(X\) is a compact measure hyperbolic space, is \(\operatorname{Aut} (X)\) finite?
(3) If \(Y\) is a compact hyperbolic complex space and \(X\) is an arbitrary compact complex space, is the set of surjective meromorphic maps \(f:X \to Y\) finite?
(4) If an algebraic manifold admits a Hermitian metric (or even a Kähler metric) with negative holomorphic sectional curvature, it is of general type?
For the entire collection see [Zbl 0771.00034].
Reviewer: A.Papadopoulos (Strasbourg)
MSC:
| 32Q45 | Hyperbolic and Kobayashi hyperbolic manifolds |
