Ohsawa, Takeo Stability of pseudoconvexity of disc bundles over compact Riemann surfaces and application to a family of Galois coverings. (English) Zbl 1325.32009 Int. J. Math. 26, No. 4, Article ID 1540003, 7 p. (2015). 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. Reviewer: Viorel Vâjâitu (Bucureşti) Cited in 2 Documents 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 32F17 Other notions of convexity in relation to several complex variables Keywords:disc bundle; compact Riemann surface; pseudoconvex; holomorphical convexity; weakly 1-complete × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.4171/PRIMS/127 · Zbl 1325.32035 · doi:10.4171/PRIMS/127 [2] DOI: 10.1007/BF01447838 · Zbl 0038.23502 · doi:10.1007/BF01447838 [3] DOI: 10.1090/S0002-9904-1960-10413-2 · Zbl 0090.05101 · doi:10.1090/S0002-9904-1960-10413-2 [4] DOI: 10.1007/BF02392263 · Zbl 0249.32014 · doi:10.1007/BF02392263 [5] DOI: 10.1307/mmj/1030132540 · Zbl 1001.32007 · doi:10.1307/mmj/1030132540 [6] Coltoiu M., Nagoya Math. J. 157 pp 1– (2000) [7] DOI: 10.1007/BF01456222 · Zbl 0502.32010 · doi:10.1007/BF01456222 [8] DOI: 10.2977/prims/1195178932 · Zbl 0601.32023 · doi:10.2977/prims/1195178932 [9] DOI: 10.2307/2373037 · Zbl 0122.40102 · doi:10.2307/2373037 [10] DOI: 10.4007/annals.2012.176.3.4 · Zbl 1273.32015 · doi:10.4007/annals.2012.176.3.4 [11] DOI: 10.2307/1970257 · Zbl 0108.07804 · doi:10.2307/1970257 [12] Katzarkov L., Ann. Sci. École Norm. Sup. 31 pp 525– (1998) [13] DOI: 10.1007/BF01244307 · Zbl 0819.14006 · doi:10.1007/BF01244307 [14] DOI: 10.1007/BF01453583 · Zbl 0733.32008 · doi:10.1007/BF01453583 [15] DOI: 10.1007/BF01934340 · Zbl 0765.32009 · doi:10.1007/BF01934340 [16] Ohsawa T., Nagoya Math. J. 142 pp 1– (1996) [17] Ohsawa T., Nagoya Math. J. 147 pp 107– (1997) · Zbl 0902.32004 · doi:10.1017/S0027763000006334 [18] Ohsawa T., Nagoya Math. J. 149 pp 1– (1998) · Zbl 0911.32027 · doi:10.1017/S0027763000006516 [19] DOI: 10.1007/978-3-642-38010-5 · Zbl 1277.14002 · doi:10.1007/978-3-642-38010-5 [20] Ueda T., J. Math. Kyoto Univ. 22 pp 583– (1983) · Zbl 0519.32019 · doi:10.1215/kjm/1250521670 [21] Vâjâitu V., C. R. Acad. Sci. 322 pp 823– (1996) [22] Yamaguchi H., J. Math. Kyoto Univ. 16 pp 71– (1976) · Zbl 0326.32007 · doi:10.1215/kjm/1250522959 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.