Local construction of complex algebraic surfaces with respect to the universal covering (Q795880)

The author studies a morphism \(\pi: X\to S\) from a smooth complex algebraic surface to a smooth complex curve which is locally trivial from the differential viewpoint. He assumes that the fundamental groups of the base and the fibre are non-commutative, and that the universal covering \(\tilde X\) is not a bidisk. He indicates the proofs for the following results: The group \(\Aut \tilde X\) of all biholomorphic automorphisms is countable. The fundamental group \(\pi_1(X)\) has finite index in \(\Aut \tilde X\). There are only finitely many subgroups of \(\Aut \tilde X\) which act properly discontinuously and are isomorphic to \(\pi_1(X)\).