On the Picard number of divisors in Fano manifolds
Cinzia Casagrande (2012)
Annales scientifiques de l'École Normale Supérieure
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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 .