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Stability of pseudoconvexity of disc bundles over compact Riemann surfaces and application to a family of Galois coverings. (English) Zbl 1325.32009
Author’s abstract: It is proved that Galois coverings of smooth families of compact Riemann surfaces over Stein manifolds are holomorphically convex if the covering transformation groups are isomorphic to discrete subgroups of the automorphism group of the unit disc. The proof is based on an extension of the fact that disc bundles over compact Kähler manifolds are weakly 1-complete.

MSC:
32D15 Continuation of analytic objects in several complex variables
32E40 The Levi problem
30F10 Compact Riemann surfaces and uniformization
32E05 Holomorphically convex complex spaces, reduction theory
32E10 Stein spaces, Stein manifolds
32F17 Other notions of convexity in relation to several complex variables
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