## Some boundedness results for Fano-like Moishezon manifolds

### Summary

Summary: 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.

### Mathematics Subject Classification

14J45, 14E30, 14E05, 32J18

### Keywords/Phrases

Fano manifolds, non projective manifold, smooth blow-down, mori theory, Hilbert scheme