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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 1, Pages 192–202 (Mi izv1423)  

This article is cited in 24 scientific papers (total in 24 papers)

On the derived category of coherent sheaves on Grassmann manifolds

M. M. Kapranov


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English version:
Mathematics of the USSR-Izvestiya, 1985, 24:1, 183–192

Bibliographic databases:

UDC: 512.7
MSC: Primary 14M15; Secondary 14F05, 18E30, 18F20
Received: 12.01.1983

Citation: M. M. Kapranov, “On the derived category of coherent sheaves on Grassmann manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 48:1 (1984), 192–202; Math. USSR-Izv., 24:1 (1985), 183–192

Citation in format AMSBIB
\Bibitem{Kap84}
\by M.~M.~Kapranov
\paper On~the derived category of coherent sheaves on Grassmann manifolds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 1
\pages 192--202
\mathnet{http://mi.mathnet.ru/izv1423}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=733363}
\zmath{https://zbmath.org/?q=an:0564.14023}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 1
\pages 183--192
\crossref{https://doi.org/10.1070/IM1985v024n01ABEH001221}


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

    This publication is cited in the following articles:
    1. A. L. Gorodentsev, “Exceptional bundles on surfaces with a moving anticanonical class”, Math. USSR-Izv., 33:1 (1989), 67–83  mathnet  crossref  mathscinet  zmath
    2. Marc Levine, V. Srinivas, Jerzy Weyman, “K-theory of twisted Grassmannians”, K-Theory, 3:2 (1989), 99  crossref  mathscinet  zmath
    3. A. I. Bondal, “Representation of associative algebras and coherent sheaves”, Math. USSR-Izv., 34:1 (1990), 23–42  mathnet  crossref  mathscinet  zmath
    4. D. Yu. Nogin, “Spirals of period 4 and equations of Markov type”, Math. USSR-Izv., 37:1 (1991), 209–226  mathnet  crossref  mathscinet  zmath  adsnasa
    5. D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Meltzer H., “Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines”, Mem. Am. Math. Soc., 171:808 (2004), III+  mathscinet  isi
    8. Costa L., Miro-Roig R.M., “Cohomological characterization of vector bundles on multiprojective spaces”, Journal of Algebra, 294:1 (2005), 73–96  crossref  isi
    9. Kawamata Yu., “Derived categories of toric varieties”, Michigan Mathematical Journal, 54:3 (2006), 517–535  crossref  isi  elib
    10. L. COSTA, R. M. MIRÓ–ROIG, “Geometric collections and Castelnuovo–Mumford regularity”, Math Proc Camb Phil Soc, 143:3 (2007)  crossref  zmath  isi
    11. Costa L., Miro-Roig R.M., “m-Blocks collections and Castelnuovo-Mumford regularity in multiprojective spaces”, Nagoya Mathematical Journal, 186 (2007), 119–155  isi
    12. Masaharu Kaneda, “Kapranov’s Tilting Sheaf on the Grassmannian in Positive Characteristic”, Algebr Represent Theor, 11:4 (2008), 347  crossref  mathscinet  zmath  isi
    13. Francesco Malaspina, “A few splitting criteria for vector bundles”, Ricerche mat, 57:1 (2008), 55  crossref  mathscinet
    14. Laura Costa, Rosa Maria Miró-Roig, “Monads and instanton bundles on smooth hyperquadrics”, Math Nachr, 282:2 (2009), 169  crossref  zmath  isi  elib
    15. A. Elagin, “Semiorthogonal decompositions of derived categories of equivariant coherent sheaves”, Izv. Math., 73:5 (2009), 893–920  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Miro-Roig, RM, “Cohomological characterisation of Steiner bundles”, Forum Mathematicum, 21:5 (2009), 871  crossref  isi
    17. A. Polishchuk, “K-theoretic exceptional collections at roots of unity”, J K-Theory, 2010, 1  crossref
    18. Yukinobu Toda, Hokuto Uehara, “Tilting generators via ample line bundles”, Advances in Mathematics, 223:1 (2010), 1  crossref
    19. Sergei A. Tikhomirov, “Stabilnye rassloeniya ranga 2 s klassami Cherna $c_1=0$, $c_2=2$ na $\mathbb P^3$ i giperkvadriki Ponsele”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 551–555  mathnet
    20. Craw A., “Quiver Flag Varieties and Multigraded Linear Series”, Duke Math. J., 156:3 (2011), 469–500  crossref  mathscinet  zmath  isi
    21. Laura Costa, Rosa Maria Miró-Roig, “Derived category of toric varieties with small Picard number”, centr.eur.j.math, 2012  crossref
    22. Bernardara M. Bolognesi M. Faenzi D., “Homological projective duality for determinantal varieties”, Adv. Math., 296 (2016), 181–209  crossref  mathscinet  zmath  isi  elib  scopus
    23. Fonarev A., Kuznetsov A., “Derived Categories of Curves as Components of Fano Manifolds”, J. Lond. Math. Soc.-Second Ser., 97:1 (2018), 24–46  crossref  isi
    24. Novakovic S., “Tilting Objects on Some Global Quotient Stacks”, J. Commut. Algebr., 10:1 (2018), 107–137  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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