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For any minimal compact complex surface S with n=b_2(S)>0 containing globalspherical shells (GSS) we study the effectiveness of the 2n parameters given bythe n blown up points. There exists a family of surfaces with GSS whichcontains as fibers S, some Inoue-Hirzebruch surface and non minimal surfaces,such that blown up points are generically effective parameters. These familiesare versal outside a non empty hypersurface T. We deduce that, for anyconfiguration of rational curves, there is a non empty open set in theOeljeklaus-Toma moduli space such that the corresponding surfaces are definedby a contracting germ in Cremona group, in particular admit a birationalstructure.

From non-K\"ahlerian surfaces to Cremona group of P^2(C)