From non-Kählerian surfaces to Cremona group of P 2 (C)

Georges Dloussky

Complex Manifolds (2014)

  • Volume: 1, Issue: 1, page 1-33, electronic only
  • ISSN: 2300-7443

Abstract

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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.

How to cite

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Georges Dloussky. " From non-Kählerian surfaces to Cremona group of P 2 (C) ." Complex Manifolds 1.1 (2014): 1-33, electronic only. <http://eudml.org/doc/276965>.

@article{GeorgesDloussky2014,
abstract = {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.},
author = {Georges Dloussky},
journal = {Complex Manifolds},
keywords = {compact complex surfaces; global spherical shells; Inoue-Hirzebruch surfaces},
language = {eng},
number = {1},
pages = {1-33, electronic only},
title = { From non-Kählerian surfaces to Cremona group of P 2 (C) },
url = {http://eudml.org/doc/276965},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Georges Dloussky
TI - From non-Kählerian surfaces to Cremona group of P 2 (C)
JO - Complex Manifolds
PY - 2014
VL - 1
IS - 1
SP - 1
EP - 33, electronic only
AB - 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.
LA - eng
KW - compact complex surfaces; global spherical shells; Inoue-Hirzebruch surfaces
UR - http://eudml.org/doc/276965
ER -

References

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