[L'image directe du faisceau dualisant relatif n'est pas nécessairement semi-ample]
Nous donnons des détails sur la démonstration du second théorème de Fujita et nous montrons que l'image directe du fibré canonique relatif d'une fibration sur une courbe B est la somme directe d'un fibré vectoriel ample et d'un fibré vectoriel unitairement plat si l'espace total X est une variété kählérienne compacte. Nous montrons en outre que V n'est en général pas semi-ample, ce qui constitue notre résultat principal.
We provide details for the proof of Fujita's second theorem and prove that for a Kähler fibre space over a smooth projective curve B, the direct image of the relative dualizing sheaf is the direct sum of an ample and a unitary flat bundle. We also show that V needs not be semiample, which is our main result.
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@article{CRMATH_2014__352_3_241_0,
author = {Catanese, Fabrizio and Dettweiler, Michael},
title = {The direct image of the relative dualizing sheaf needs not be semiample},
journal = {Comptes Rendus. Math\'ematique},
pages = {241--244},
publisher = {Elsevier},
volume = {352},
number = {3},
year = {2014},
doi = {10.1016/j.crma.2013.12.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.12.015/}
}
TY - JOUR AU - Catanese, Fabrizio AU - Dettweiler, Michael TI - The direct image of the relative dualizing sheaf needs not be semiample JO - Comptes Rendus. Mathématique PY - 2014 SP - 241 EP - 244 VL - 352 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.12.015/ DO - 10.1016/j.crma.2013.12.015 LA - en ID - CRMATH_2014__352_3_241_0 ER -
%0 Journal Article %A Catanese, Fabrizio %A Dettweiler, Michael %T The direct image of the relative dualizing sheaf needs not be semiample %J Comptes Rendus. Mathématique %D 2014 %P 241-244 %V 352 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.12.015/ %R 10.1016/j.crma.2013.12.015 %G en %F CRMATH_2014__352_3_241_0
Catanese, Fabrizio; Dettweiler, Michael. The direct image of the relative dualizing sheaf needs not be semiample. Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 241-244. doi : 10.1016/j.crma.2013.12.015. http://www.numdam.org/articles/10.1016/j.crma.2013.12.015/
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