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Trudy Mat. Inst. Steklova, 2009, Volume 264, Pages 116–128 (Mi tm800)  

This article is cited in 17 scientific papers (total in 17 papers)

Derived Categories of Fano Threefolds

A. G. Kuznetsovab

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Laboratoire J.-V. Poncelet, Independent University of Moscow, Moscow, Russia

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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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 264, 110–122

Bibliographic databases:

UDC: 512.7
Received in September 2008

Citation: A. G. Kuznetsov, “Derived Categories of Fano Threefolds”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 116–128; Proc. Steklov Inst. Math., 264 (2009), 110–122

Citation in format AMSBIB
\by A.~G.~Kuznetsov
\paper Derived Categories of Fano Threefolds
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 116--128
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 264
\pages 110--122

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    This publication is cited in the following articles:
    1. Kuznetsov A., “Instanton Bundles on Fano Threefolds”, Cent. Eur. J. Math., 10:4 (2012), 1198–1231  crossref  mathscinet  zmath  isi  elib  scopus
    2. Costa L., Maria Miro-Roig R., “Derived Category of Toric Varieties with Small Picard Number”, Cent. Eur. J. Math., 10:4 (2012), 1280–1291  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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
    4. Bernardara M. Bolognesi M., “Derived Categories and Rationality of Conic Bundles”, Compos. Math., 149:11 (2013), 1789–1817  crossref  mathscinet  zmath  isi  elib  scopus
    5. Iliev A., Katzarkov L., Przyjalkowski V., “Double Solids, Categories and Non-Rationality”, Proc. Edinb. Math. Soc., 57:1 (2014), 145–173  crossref  mathscinet  zmath  isi  elib  scopus
    6. Tabuada G., “Weil Restriction of Noncommutative Motives”, J. Algebra, 430 (2015), 119–152  crossref  mathscinet  zmath  isi  elib  scopus
    7. Bernardara M., Tabuada C., “Relations Between the Chow Motive and the Noncommutative Motive of a Smooth Projective Variety”, J. Pure Appl. Algebr., 219:11 (2015), 5068–5077  crossref  mathscinet  zmath  isi  elib  scopus
    8. Marcello Bernardara, Gonçalo Tabuada, “From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives”, Mosc. Math. J., 16:2 (2016), 205–235  mathnet  crossref  mathscinet
    9. Bernardara M. Bolognesi M. Faenzi D., “Homological projective duality for determinantal varieties”, Adv. Math., 296 (2016), 181–209  crossref  mathscinet  zmath  isi  elib  scopus
    10. Lee K.-S., “Exceptional sequences of maximal length on some surfaces isogenous to a higher product”, J. Algebra, 454 (2016), 308–333  crossref  mathscinet  zmath  isi  elib  scopus
    11. Kuznetsov A., “Derived Categories View on Rationality Problems”, Rationality Problems in Algebraic Geometry, Lect. Notes Math., Lecture Notes in Mathematics, 2172, ed. Pardini R. Pirola G., Springer International Publishing Ag, 2016, 67–104  crossref  mathscinet  isi  scopus
    12. Kiem Y.-H., Kim I.-K., Lee H., Lee K.-S., “All complete intersection varieties are Fano visitors”, Adv. Math., 311 (2017), 649–661  crossref  mathscinet  zmath  isi  scopus
    13. Belmans P., Raedschelders T., “Embeddings of Algebras in Derived Categories of Surfaces”, Proc. Amer. Math. Soc., 145:7 (2017), 2757–2770  crossref  mathscinet  zmath  isi  scopus
    14. Auel A., Bernardara M., “Cycles, Derived Categories, and Rationality”, Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 95, eds. Coskun I., DeFernex T., Gibney A., Amer Mathematical Soc, 2017, 199–266  crossref  mathscinet  zmath  isi  scopus
    15. Kuznetsov A.G., Prokhorov Yu.G., Shramov C.A., “Hilbert Schemes of Lines and Conics and Automorphism Groups of Fano Threefolds”, Jap. J. Math., 13:1 (2018), 109–185  crossref  mathscinet  zmath  isi  scopus
    16. Kuznetsov A., Perry A., “Derived Categories of Gushel-Mukai Varieties”, Compos. Math., 154:7 (2018), 1362–1406  crossref  mathscinet  isi
    17. Liu W., Yang S., Yu X., “Classification of Full Exceptional Collections of Line Bundles on Three Blow-Ups of P-3”, J. Korean. Math. Soc., 56:2 (2019), 387–419  crossref  mathscinet  isi  scopus
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