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.
@article{bwmeta1.element.doi-10_2478_coma-2014-0001,
author = {Georges Dloussky},
title = {
From non-K\"ahlerian surfaces to Cremona group of P
2
(C)
},
journal = {Complex Manifolds},
volume = {1},
year = {2014},
zbl = {1320.32022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_coma-2014-0001}
}
Georges Dloussky.
From non-Kählerian surfaces to Cremona group of P
2
(C)
. Complex Manifolds, Tome 1 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_coma-2014-0001/
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