Geodesic
Derived Categories of Fano Threefolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 116-128.

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We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In the appendix we discuss how the ring of algebraic cycles of a smooth projective variety is related to the Grothendieck group of its derived category. 
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A. G. Kuznetsov. Derived Categories of Fano Threefolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Multidimensional algebraic geometry, Tome 264 (2009), pp. 116-128. http://geodesic.mathdoc.fr/item/TM_2009_264_a13/

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