[Fibrations en surfaces de del Pezzo obtenues par éclatement d'une courbe lisse dans une variété projective]
Cette Note est consacrée à l'étude des variétés de Fano X obtenues par éclatement d'une courbe lisse C dans une variété projective complexe et lisse Y. D'après la théorie de Mori, on peut assurer l'existence d'une contraction extrémale différente de l'éclatement . Ici, on donne la classification complète des paires correspondantes dans le cas où φ est de type fibrant de dimension relative 2, c'est-à-dire quand les fibres générales de φ sont des surfaces de del Pezzo. Dans Tsukioka (thèse, université Nancy 1, 2005) le cas de dimension relative 1 est aussi étudié.
This Note is devoted to the study of the Fano manifolds X obtained by blow-up along a smooth curve C in a complex projective manifold Y. By the Mori theory, we can ensure the existence of an extremal contraction different from the blow-up . Here we give the complete classification of the corresponding pairs in the case where φ is a fiber type contraction of relative dimension 2, i.e. the general fibers of φ are del Pezzo surfaces. In Tsukioka (Thesis, Nancy University 1, 2005), the relative dimension 1 case is also considered.
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@article{CRMATH_2005__340_8_581_0,
author = {Tsukioka, Toru},
title = {Del {Pezzo} surface fibrations obtained by blow-up of a smooth curve in a projective manifold},
journal = {Comptes Rendus. Math\'ematique},
pages = {581--586},
publisher = {Elsevier},
volume = {340},
number = {8},
year = {2005},
doi = {10.1016/j.crma.2005.03.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.03.004/}
}
TY - JOUR AU - Tsukioka, Toru TI - Del Pezzo surface fibrations obtained by blow-up of a smooth curve in a projective manifold JO - Comptes Rendus. Mathématique PY - 2005 SP - 581 EP - 586 VL - 340 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.03.004/ DO - 10.1016/j.crma.2005.03.004 LA - en ID - CRMATH_2005__340_8_581_0 ER -
%0 Journal Article %A Tsukioka, Toru %T Del Pezzo surface fibrations obtained by blow-up of a smooth curve in a projective manifold %J Comptes Rendus. Mathématique %D 2005 %P 581-586 %V 340 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.03.004/ %R 10.1016/j.crma.2005.03.004 %G en %F CRMATH_2005__340_8_581_0
Tsukioka, Toru. Del Pezzo surface fibrations obtained by blow-up of a smooth curve in a projective manifold. Comptes Rendus. Mathématique, Tome 340 (2005) no. 8, pp. 581-586. doi : 10.1016/j.crma.2005.03.004. http://www.numdam.org/articles/10.1016/j.crma.2005.03.004/
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