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Complex Manifolds

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From non-Kählerian surfaces to Cremona group of P2(C)

Georges Dloussky
Published Online: 2014-04-23 | DOI: https://doi.org/10.2478/coma-2014-0001


For any minimal compact complex surface S with n = b2(S) > 0 containing global spherical shells (GSS) we study the effectiveness of the 2n parameters given by the n blown up points. There exists a family of surfaces S → B with GSS which contains as fibers S, some Inoue-Hirzebruch surface and non minimal surfaces, such that blown up points are generically effective parameters. These families are versal outside a non empty hypersurface T ⊂ B. We deduce that, for any configuration of rational curves, there is a non empty open set in the Oeljeklaus-Toma moduli space such that the corresponding surfaces are defined by a contracting germ in Cremona group, in particular admit a birational structure.


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About the article

Received: 2013-11-03

Accepted: 2014-02-11

Published Online: 2014-04-23

Published in Print: 2014-01-01

Citation Information: Complex Manifolds, Volume 1, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.2478/coma-2014-0001.

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© 2014 Georges Dloussky. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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