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Derived Categories View on Rationality Problems

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Rationality Problems in Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2172))

Abstract

We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds.

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Acknowledgements

Alexander Kuznetsov was partially supported by the Russian Academic Excellence Project “5-100”, by RFBR grants 14-01-00416, 15-01-02164, 15-51-50045, and by the Simons foundation. Some steps towards understanding geometry of these fourfolds was made in [K15a].

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Authors and Affiliations

  1. Algebraic Geometry Section, Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin Str., Moscow, 119991, Russia

    Alexander Kuznetsov

  2. The Poncelet Laboratory, Independent University of Moscow, Moscow, Russia

    Alexander Kuznetsov

  3. Laboratory of Algebraic Geometry, National Research University Higher School of Economics, Moscow, Russia

    Alexander Kuznetsov

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  1. Alexander Kuznetsov
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Correspondence to Alexander Kuznetsov .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa Dipartimento di Matematica, Pisa, Italy

    Rita Pardini

  2. Dipartimento di matematica, University of Pavia, Pavia, Italy

    Gian Pietro Pirola

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Kuznetsov, A. (2016). Derived Categories View on Rationality Problems. In: Pardini, R., Pirola, G. (eds) Rationality Problems in Algebraic Geometry. Lecture Notes in Mathematics(), vol 2172. Springer, Cham. https://doi.org/10.1007/978-3-319-46209-7_3

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