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Zbl 0783.32008
Dloussky, Georges
Filling in holes of analytic surfaces and classification of compact surfaces. (Colmatage de surfaces holomorphes et classification des surfaces compactes.) (French)
[J] Ann. Inst. Fourier 43, No.3, 713-741 (1993). ISSN 0373-0956; ISSN 1777-5310/e

We consider the problem of filling in holes in dimension 2 where we examine under which condition a strictly pseudoconvex hypersurface in an analytic surface is the boundary of a Stein space. We show that Rossi's example of a strictly pseudoconvex hypersurface $\Sigma$, which bounds two nonrelatively compact domains, is not the boundary of a Stein space although holomorphic functions in a neighbourhood of $\Sigma$ give local charts. We show that in a compact complex surface $S$ without nonconstant meromorphic functions with $b\sb 1(S)=1$, such a phenomenon cannot exist.
[G.Dloussky (Nice)]

MSC 2000:: *32E10 Stein spaces and manifolds
32F10 $q$-convexity, etc.
32J15 Compact surfaces (analytic spaces)

Keywords: classification of surfaces; filling in holes; strictly pseudoconvex hypersurface; analytic surface; boundary of a Stein space; compact complex surface

Cited in: Zbl 1149.32011

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