On the problems of Hartshorne and Serre for some -analytic surfaces |
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| Institution: | 1. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;2. Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland;1. Department of Mathematics, University of California, Los Angeles, CA 90095, USA;2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Department of Mathematics, Harvard University, Cambridge, MA 02138, USA |
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| Abstract: | Let M be a compact -analytic surface, let Γ ⊂ M be a compact analytic subvariety, and let X := Mx00393;. We are interested in the following two problems: Assume that X does not contain any compact curve and that Γ is an irreducible compact curve such that Γ2 ≥ 0 (resp. assume that the analytic cohomology groups H1 (X, Ωp) = 0, for all 0 ≤ p ≤ 2). Is X always Stein? It is our main purpose here to provide an affirmative answer to those two problems, provided M is either a (minimal) ruled surface or a non-algebraic compact surface. Also, the affine structure of such Stein surfaces will be discussed. |
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