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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 \(D\).

14J45 Fano varieties
14E30 Minimal model program (Mori theory, extremal rays)
Full Text: DOI arXiv
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