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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)
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