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Derived categories of Fano threefolds

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Abstract

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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Authors and Affiliations

  1. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. G. Kuznetsov

  2. The Poncelet Laboratory, Independent University of Moscow, Bol’shoi Vlas’evskii per. 11, Moscow, 119002, Russia

    A. G. Kuznetsov

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  1. A. G. Kuznetsov
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Correspondence to A. G. Kuznetsov.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 116–128.

In memory of V.A. Iskovskikh

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Kuznetsov, A.G. Derived categories of Fano threefolds. Proc. Steklov Inst. Math. 264, 110–122 (2009). https://doi.org/10.1134/S0081543809010143

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