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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 264, Pages 116–128 (Mi tm800)

This article is cited in 32 scientific papers (total in 32 papers)

Derived Categories of Fano Threefolds

A. G. Kuznetsov^ab

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

Full-text PDF (247 kB) Citations (32)

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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.

Received in September 2008

English version:
Proceedings of the Steklov Institute of Mathematics, 2009, Volume 264, Pages 110–122
DOI: https://doi.org/10.1134/S0081543809010143

Bibliographic databases:

Document Type: Article

UDC: 512.7

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/tm800

https://www.mathnet.ru/eng/tm/v264/p116

This publication is cited in the following 32 articles:

Xun Lin, Shizhuo Zhang, “Kuznetsov's Fano threefold conjecture via Hochschild–Serre algebra”, Math. Z., 308:2 (2024)
Soheyla Feyzbakhsh, Zhiyu Liu, Shizhuo Zhang, “new perspectives on categorical Torelli theorems for del Pezzo threefolds”, Journal de Mathématiques Pures et Appliquées, 2024, 103627
Arend Bayer, Alexander Perry, “Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2023
Xuqiang QIN, “Bridgeland stability of minimal instanton bundles on Fano threefolds”, J. Math. Soc. Japan, 75:4 (2023)
Laura Pertusi, Ethan Robinett, “Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor”, Mathematische Nachrichten, 296:7 (2023), 2975
Augustinas Jacovskis, Xun Lin, Zhiyu Liu, Shizhuo Zhang, “Infinitesimal categorical Torelli theorems for Fano threefolds”, Journal of Pure and Applied Algebra, 227:12 (2023), 107418
Young-Hoon Kiem, Kyoung-Seog Lee, Springer Proceedings in Mathematics & Statistics, 409, Birational Geometry, Kähler–Einstein Metrics and Degenerations, 2023, 517
Fei Xie, “Nodal quintic del Pezzo threefolds and their derived categories”, Math. Z., 304:3 (2023)
Nunez P., “A Note on Semiorthogonal Decompositions For Fano Fibrations”, Geod. Dedic., 216:2 (2022), 20
Ciliberto C. Zaidenberg M., “Lines, Conics, and All That”, Pure Appl. Math. Q., 18:1 (2022), 101–176
Zhiyu Liu, Shizhuo Zhang, “A note on Bridgeland moduli spaces and moduli spaces of sheaves on $X_{14}$ and $Y_3$ ”, Math. Z., 302:2 (2022), 803
Kuznetsov A., Prokhorov Yu., “Rationality of Mukai Varieties Over Non-Closed Fields”, Rationality of Varieties, Progress in Mathematics, 342, eds. Farkas G., VanDerGeer G., Shen M., Taelman L., Birkhauser Verlag Ag, 2021, 249–290
Pertusi L. Yang S., “Some Remarks on Fano Three-Folds of Index Two and Stability Conditions”, Int. Math. Res. Notices, 2021, rnaa387
Laterveer R., “Algebraic Cycles and Fano Threefolds of Genus 8”, Port Math., 78:3-4 (2021), 255–280
Bayer A., Lahoz M., Macri E., Nuer H., Perry A., Stellari P., “Stability Conditions in Families”, Publ. Math. IHES, 133:1 (2021), 157–325
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
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
Kuznetsov A., Perry A., “Derived Categories of Gushel-Mukai Varieties”, Compos. Math., 154:7 (2018), 1362–1406
Kiem Y.-H., Kim I.-K., Lee H., Lee K.-S., “All complete intersection varieties are Fano visitors”, Adv. Math., 311 (2017), 649–661
Belmans P., Raedschelders T., “Embeddings of Algebras in Derived Categories of Surfaces”, Proc. Amer. Math. Soc., 145:7 (2017), 2757–2770

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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