Classification of Fano manifolds containing a negative divisor isomorphic to projective space

We classify n-dimensional complex Fano manifolds X (n >= 3) containing a divisor E isomorphic to Pn-1 such that deg N-E/X is strictly negative. Our main tool is the extremal contraction theory together with numerical arguments on intersection numbers of divisors on X. In the last section, we consider, more generally, Fano manifolds X containing a prime divisor with Picard number one, and show that the Picard number of such X is less than or equal to three.