The Bondal-Orlov Reconstruction Theorem

The Bondal-Orlov Reconstraction Theorem says that is possible to reconstruct a smooth projective variety X from its derived category of coherent sheaves. More precisely, under the fundamental assumption on the (anti-)ampleness of the canonical sheaf of X, it is enough to have an equivalence between the derived categories of coherent sheaves on X and on another smooth projective variety Y, to deduce directly an isomorphism between the underlined varieties X and Y.