From non-Kählerian surfaces to Cremona group of P^2(C)
Abstract
For any minimal compact complex surface $S$ with $b_2(S)>0$ containing global spherical shells (GSS) there exists a family of surfaces $\cal S\to B$ 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 $T\subset B$. In case of surfaces with a cycle and one tree of rational curves we give new normal forms of contracting germs in Cremona group $Bir(\bb P^2(\bb C))$ and show that they admit a birational structure. These families contain all possible surfaces, in particular all surfaces $S$ with GSS and $0
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Georges Dloussky : Connect in order to contact the contributor
https://hal.science/hal-00707355
Submitted on : Tuesday, June 12, 2012-3:11:21 PM
Last modification on : Friday, March 24, 2023-2:52:55 PM
Long-term archiving on: Thursday, December 15, 2016-1:34:44 PM
Cite
Georges Dloussky. From non-Kählerian surfaces to Cremona group of P^2(C). Journal of complex manifolds, 2014, 1, pp.1-33. ⟨hal-00707355⟩
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