We give a generalization of the theorem of Bondal and Orlov about the derived categories of coherent sheaves on intersections of quadrics revealing its relation to projective duality. As an application we describe the derived categories of coherent sheaves on Fano 3-folds of index 1 and degrees 12, 16 and 18.
Some remarks on the derived categories of coherent sheaves on homogeneous spaces
Algebraization of complex analytic varieties and derived categories
Some examples of spaces of stability conditions on derived categories
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