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

This article is cited in 54 scientific papers (total in 54 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

Full text: PDF file (1400 kB)
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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
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    This publication is cited in the following articles:
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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
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    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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    15. Bernardara M. Bolognesi M., “Categorical Representability and Intermediate Jacobians of Fano Threefolds”, Derived Categories in Algebraic Geometry - Tokyo 2011, EMS Ser. Congr. Rep., ed. Kawamata Y., Eur. Math. Soc., 2012, 1–25  mathscinet  zmath  isi
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    19. Bayer A., Macri E., “Projectivity and Birational Geometry of Bridgeland Moduli Spaces”, J. Am. Math. Soc., 27:3 (2014), 707–752  crossref  mathscinet  zmath  isi  scopus
    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
    21. Meachan C., “Derived Autoequivalences of Generalised Kummer Varieties”, Math. Res. Lett., 22:4 (2015), 1193–1221  crossref  mathscinet  zmath  isi  elib  scopus
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    23. Lombardi L., Tirabassi S., “Deformations of minimal cohomology classes on abelian varieties”, Commun. Contemp. Math., 18:4 (2016), 1550066  crossref  mathscinet  zmath  isi  elib  scopus
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