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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 4, Pages 57–70 (Mi izv8339)  

This article is cited in 14 scientific papers (total in 14 papers)

On Küchle varieties with Picard number greater than 1

A. G. Kuznetsov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We describe the geometry of Küchle varieties (that is, Fano fourfolds of index 1 contained in Grassmannians as zero loci of sections of equivariant vector bundles) with Picard number greater than 1. We also describe the structure of their derived categories.

Keywords: Fano varieties, special varieties, semiorthogonal decompositions of derived categories.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.4213/im8339

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English version:
Izvestiya: Mathematics, 2015, 79:4, 698–709

Bibliographic databases:

UDC: 512.7
MSC: 14J35, 14J45, 14M15
Received: 19.01.2015

Citation: A. G. Kuznetsov, “On Küchle varieties with Picard number greater than 1”, Izv. RAN. Ser. Mat., 79:4 (2015), 57–70; Izv. Math., 79:4 (2015), 698–709

Citation in format AMSBIB
\by A.~G.~Kuznetsov
\paper On K\"uchle varieties with Picard number greater than~1
\jour Izv. RAN. Ser. Mat.
\yr 2015
\vol 79
\issue 4
\pages 57--70
\jour Izv. Math.
\yr 2015
\vol 79
\issue 4
\pages 698--709

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  • https://doi.org/10.4213/im8339
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    This publication is cited in the following articles:
    1. Fatighenti E., “Surfaces of General Type With Pg=1, Q=0, K2=6 and Grassmannians”, Math. Nachr.  crossref  isi
    2. Fonarev A., “On the Bounded Derived Category of Igr(3,7)”, Transform. Groups  crossref  isi
    3. Victor V. Przyjalkowski, Constantin A. Shramov, “Double quadrics with large automorphism groups”, Proc. Steklov Inst. Math., 294 (2016), 154–175  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Anton Fonarev, “Irreducible Ulrich bundles on isotropic Grassmannians”, Mosc. Math. J., 16:4 (2016), 711–726  mathnet  crossref  mathscinet
    5. A. Kuznetsov, “Küchle fivefolds of type c5”, Math. Z., 284:3 (2016), 1245–1278  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    6. C. Shramov, V. Przyjalkowski, “Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes”, Bull. Korean Math. Soc., 54:5 (2017), 1527–1575 , arXiv: 1409.3729  mathnet  crossref  mathscinet  isi  scopus
    7. S. Gorchinskiy, “Integral Chow motives of threefolds with $K$-motives of unit type”, Bull. Korean Math. Soc., 54:5 (2017), 1827–1849 , arXiv: 1703.06977  mathnet  crossref  isi  scopus
    8. A. G. Kuznetsov, Yu. G. Prokhorov, C. A. Shramov, “Hilbert schemes of lines and conics and automorphism groups of Fano threefolds”, Jpn. J. Math., 13:1 (2018), 109–185  crossref  mathscinet  zmath  isi  scopus
    9. A. Kuznetsov, A. Perry, “Derived categories of Gushel-Mukai varieties”, Compos. Math., 154:7 (2018), 1362–1406  crossref  mathscinet  isi
    10. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. D. Inoue, A. Ito, M. Miura, “Complete intersection Calabi-Yau manifolds with respect to homogeneous vector bundles on grassmannians”, Math. Z., 292:1-2 (2019), 677–703  crossref  isi
    12. A. Kuznetsov, “Calabi-Yau and fractional Calabi-Yau categories”, J. Reine Angew. Math., 753 (2019), 239–267  crossref  isi
    13. R. Laterveer, “A Remark on the Chowring of Kuchle Fourfolds of Type D3”, Bull. Aust. Math. Soc., 100:3 (2019), 410–418  crossref  isi
    14. V. Przyjalkowski, C. Shramov, “Hodge level for weighted complete intersections”, Collect. Math., 71:3 (2020), 549–574  crossref  mathscinet  zmath  isi
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