The disk property of coverings of 1-convex surfaces
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- by Mihnea Colţoiu and Cezar Joiţa PDF
- Proc. Amer. Math. Soc. 140 (2012), 575-580 Request permission
Abstract:
Let $X$ be a 1-convex surface and $p:\tilde X\to X$ an (unbranched) covering map. We prove that if $\tilde X$ does not contain an infinite Nori string of rational curves, then $\tilde X$ satisfies the discrete disk property.References
- Mihnea Colţoiu, Coverings of $1$-convex manifolds with $1$-dimensional exceptional set, Comment. Math. Helv. 68 (1993), no. 3, 469–479. MR 1236764, DOI 10.1007/BF02565830
- M. Coltoiu and K. Diederich, On the coverings of proper families of 1-dimensional complex spaces, Michigan Math. J. 47 (2000), no. 2, 369–375. MR 1793631, DOI 10.1307/mmj/1030132540
- Mihnea Colţoiu and Mihai Tibăr, On the disk theorem, Math. Ann. 345 (2009), no. 1, 175–183. MR 2520056, DOI 10.1007/s00208-009-0346-4
- Ferdinand Docquier and Hans Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94–123 (German). MR 148939, DOI 10.1007/BF01360084
- Albrecht Dold, Lectures on algebraic topology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1972 edition. MR 1335915, DOI 10.1007/978-3-642-67821-9
- John Erik Fornaess, $2$ dimensional counterexamples to generalizations of the Levi problem, Math. Ann. 230 (1977), no. 2, 169–173. MR 486625, DOI 10.1007/BF01370661
- Klaus Fritzsche and Hans Grauert, From holomorphic functions to complex manifolds, Graduate Texts in Mathematics, vol. 213, Springer-Verlag, New York, 2002. MR 1893803, DOI 10.1007/978-1-4684-9273-6
- Terrence Napier, Convexity properties of coverings of smooth projective varieties, Math. Ann. 286 (1990), no. 1-3, 433–479. MR 1032941, DOI 10.1007/BF01453583
- Raghavan Narasimhan, The Levi problem for complex spaces. II, Math. Ann. 146 (1962), 195–216. MR 182747, DOI 10.1007/BF01470950
Additional Information
- Mihnea Colţoiu
- Affiliation: “Simion Stoilow” Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, Bucharest 014700, Romania
- Email: Mihnea.Coltoiu@imar.ro
- Cezar Joiţa
- Affiliation: “Simion Stoilow” Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, Bucharest 014700, Romania
- Email: Cezar.Joita@imar.ro
- Received by editor(s): November 23, 2010
- Published electronically: June 9, 2011
- Additional Notes: Both authors were partially supported by CNCSIS Grant PN-II ID_1185, contract 472/2009.
- Communicated by: Franc Forstneric
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 575-580
- MSC (2010): Primary 32F17, 32F10, 32E05, 32E10
- DOI: https://doi.org/10.1090/S0002-9939-2011-11005-0
- MathSciNet review: 2846325