an:06476698
Zbl 1320.32022
Dloussky, Georges
From non-K??hlerian surfaces to Cremona group of \(\mathbb{P}^2(\mathbb{C})\)
EN
Complex Manifolds 1, 1-33 (2014).
00347707
2014
j
32J15
compact complex surfaces; global spherical shells; Inoue-Hirzebruch surfaces
Summary: For any minimal compact complex surface \(S\) with \(n = b_{2}(S) > 0\) 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 \(\mathcal{S} \to B\) 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 \(T \subset B\). 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.