Some Boundedness Results for Fano-Like Moishezon Manifolds

We prove finiteness of the number of smooth blow-downs on Fano manifolds and boundedness results for the geometry of non projective Fano-like manifolds. Our proofs use properness of Hilbert schemes and Mori theory.

1991 Mathematics Subject Classification: 14J45, 14E30, 14E05, 32J18.

Keywords and Phrases: Fano manifolds, non projective manifold, smooth blow-down, Mori theory, Hilbert scheme.

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