Let be a complex Fano manifold of arbitrary dimension, and a prime divisor in . We consider the image of in under the natural push-forward of -cycles. We show that . Moreover if , then either where is a Del Pezzo surface, or and has a fibration in Del Pezzo surfaces onto a Fano manifold such that .
Soient une variété de Fano lisse et complexe de dimension arbitraire, et un diviseur premier dans . Nous considérons l’image de dans par l’application naturelle de push-forward de -cycles. Nous démontrons que . De plus, si , alors soit où est une surface de Del Pezzo, soit et a une fibration en surfaces de Del Pezzo sur une variété de Fano lisse , telle que .
Keywords: Fano varieties, Mori theory, extremal rays
Mot clés : variétés de Fano, théorie de Mori, rayons extrêmaux
@article{ASENS_2012_4_45_3_363_0, author = {Casagrande, Cinzia}, title = {On the {Picard} number of divisors in {Fano} manifolds}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {363--403}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 45}, number = {3}, year = {2012}, doi = {10.24033/asens.2168}, mrnumber = {3014481}, zbl = {1267.14050}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2168/} }
TY - JOUR AU - Casagrande, Cinzia TI - On the Picard number of divisors in Fano manifolds JO - Annales scientifiques de l'École Normale Supérieure PY - 2012 SP - 363 EP - 403 VL - 45 IS - 3 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2168/ DO - 10.24033/asens.2168 LA - en ID - ASENS_2012_4_45_3_363_0 ER -
%0 Journal Article %A Casagrande, Cinzia %T On the Picard number of divisors in Fano manifolds %J Annales scientifiques de l'École Normale Supérieure %D 2012 %P 363-403 %V 45 %N 3 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2168/ %R 10.24033/asens.2168 %G en %F ASENS_2012_4_45_3_363_0
Casagrande, Cinzia. On the Picard number of divisors in Fano manifolds. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 3, pp. 363-403. doi : 10.24033/asens.2168. http://www.numdam.org/articles/10.24033/asens.2168/
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