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Oct 25, 2013 at 17:52 comment added Benoit There is also another paper by A. Nadel which is linked with this topic (\emph{Semisimplicity of the group of biholomorphisms of the universal covering of a compact complex manifold with ample canonical bundle}). In this really beautiful paper Nadel shwos for instance that the automorphism groups of the universal cover a canonically polarized surface (it is the case for a Kodaira surface) are very constraints: if it's positive dimensional, it's the automorphism group of the ball or of the bidisk (else it's a discrete group and it reduces almost to the fundamental group of the surface).
Oct 22, 2013 at 20:11 comment added Darius Math Very beautiful answer ! Thank you and I'm very glad to be the first one who receives an answer from you professor Catanese.
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Oct 20, 2013 at 21:36
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Oct 20, 2013 at 21:22
Oct 20, 2013 at 21:01 history answered Fabrizio Catanese CC BY-SA 3.0