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Complex manifolds whose blow-up at a point is Fano. (Variétés complexes dont l’éclatée en un point est de Fano.) (French. Abridged English version) Zbl 1036.14020
Summary: We classify complex projective manifolds \(X\) for which there exists a point \(a\) such that the blow-up of \(X\) at \(a\) is Fano. As a consequence, we get that, in dimension greater or equal than three, the quadric is the only complex manifold \(X\) for which there exists two distinct points \(a\) and \(b\) such that the blow-up of \(X\) with center \(\{a,b\}\) is Fano.

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