On the disk theorem |
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Authors: | Mihnea Col?oiu and Mihai Tib?r |
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Institution: | (1) Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucureşti, Romania;(2) Mathématiques, UMR 8524 CNRS, Université de Lille 1, 59655 Villeneuve d’Ascq, France |
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Abstract: | We construct an example of a 2-dimensional Stein normal space X with one singular point x
0 such that X\{x
0} is simply connected and it satisfies the disk condition. This answers a question raised by Forn?ss and Narasimhan. We also
prove that any increasing union of Stein open sets contained in a Stein space of dimension 2 satisfies the disk condition.
Starting from the above example we exhibit, without using deformation theory, a new type of 2-dimensional holes which cannot
be filled. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 32E10 32E40 32F10 |
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