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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 3, Pages 23–128 (Mi izv556)  

This article is cited in 55 scientific papers (total in 55 papers)

Hyperplane sections and derived categories

A. G. Kuznetsov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give a generalization of the theorem of Bondal and Orlov about the derived categories of coherent sheaves on intersections of quadrics, revealing the relation of this theorem 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.

DOI: https://doi.org/10.4213/im556

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English version:
Izvestiya: Mathematics, 2006, 70:3, 447–547

Bibliographic databases:

UDC: 512.73
MSC: 18E30, 14A22
Received: 26.04.2005
Revised: 12.09.2005

Citation: A. G. Kuznetsov, “Hyperplane sections and derived categories”, Izv. RAN. Ser. Mat., 70:3 (2006), 23–128; Izv. Math., 70:3 (2006), 447–547

Citation in format AMSBIB
\by A.~G.~Kuznetsov
\paper Hyperplane sections and derived categories
\jour Izv. RAN. Ser. Mat.
\yr 2006
\vol 70
\issue 3
\pages 23--128
\jour Izv. Math.
\yr 2006
\vol 70
\issue 3
\pages 447--547

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    1. Shinder E., Zhang Z., “L-Equivalence For Degree Five Elliptic Curves, Elliptic Fibrations and K3 Surfaces”, Bull. London Math. Soc.  crossref  mathscinet  isi
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    4. Kuznetsov A., “Derived categories of quadric fibrations and intersections of quadrics”, Adv. Math., 218:5 (2008), 1340–1369  crossref  mathscinet  zmath  isi  elib  scopus
    5. Sawon J., “Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds”, Adv. Math., 218:3 (2008), 828–864  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kuznetsov A., “Lefschetz decompositions and categorical resolutions of singularities”, Selecta Math. (N.S.), 13:4 (2008), 661–696  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. G. Kuznetsov, “Derived Categories of Fano Threefolds”, Proc. Steklov Inst. Math., 264 (2009), 110–122  mathnet  crossref  mathscinet  isi  elib  elib
    8. Macri E., Stellari P., “Infinitesimal Derived Torelli Theorem for K3 Surfaces”, with an Appendix by Sukhendu Mehrotra, Internat. Math. Res. Notices, 2009, no. 17, 3190–3220  crossref  mathscinet  zmath  isi  elib  scopus
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    20. Abuaf R., “Wonderful Resolutions and Categorical Crepant Resolutions of Singularities”, J. Reine Angew. Math., 708 (2015), 115–141  crossref  mathscinet  zmath  isi  elib  scopus
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    24. Bernardara M. Bolognesi M. Faenzi D., “Homological projective duality for determinantal varieties”, Adv. Math., 296 (2016), 181–209  crossref  mathscinet  zmath  isi  elib  scopus
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    28. Hirano Yu., “Derived Knorrer Periodicity and Orlov'S Theorem For Gauged Landau-Ginzburg Models”, Compos. Math., 153:5 (2017), 973–1007  crossref  mathscinet  zmath  isi  scopus
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    30. Auel A. Bernardara M., “Cycles, Derived Categories, and Rationality”, Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 95, ed. Coskun I. DeFernex T. Gibney A., Amer Mathematical Soc, 2017, 199–266  crossref  mathscinet  zmath  isi  scopus
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