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Classification of Fano manifolds containing a negative divisor isomorphic to projective space. (English) Zbl 1121.14036
The paper under review studies Fano manifold $$X$$ containing a divisor $$D\simeq {\mathbb P}^{n-1}$$ with $$D_{| D}\sim {\mathcal O}(-d)$$ for some positive integer $$d$$. The result is a short list of essentially three cases. The idea is to study the contraction associated to an extremal ray transverse to the divisor $$D$$.

##### MSC:
 14J45 Fano varieties 14E30 Minimal model program (Mori theory, extremal rays)
##### Keywords:
Fano varieties; extremal rays; Mori theory
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##### References:
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