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Trudy Mat. Inst. Steklova, 2015, Volume 290, Pages 80–94 (Mi tm3641)  

This article is cited in 15 scientific papers (total in 15 papers)

Geometric realizations of quiver algebras

D. O. Orlov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We construct strong exceptional collections of vector bundles on smooth projective varieties that have a prescribed endomorphism algebra. We prove that the construction problem always has a solution. We consider some applications to noncommutative projective planes and to the quiver connected with the three-point Ising function.

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


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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 70–83

Bibliographic databases:

ArXiv: 1503.03174
UDC: 512.7
Received: March 15, 2015

Citation: D. O. Orlov, “Geometric realizations of quiver algebras”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Trudy Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 80–94; Proc. Steklov Inst. Math., 290:1 (2015), 70–83

Citation in format AMSBIB
\by D.~O.~Orlov
\paper Geometric realizations of quiver algebras
\inbook Modern problems of mathematics, mechanics, and mathematical physics
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 290
\pages 80--94
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 290
\issue 1
\pages 70--83

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    This publication is cited in the following articles:
    1. Fonarev A., “On the Bounded Derived Category of Igr(3,7)”, Transform. Groups  crossref  isi
    2. D. O. Orlov, “Gluing of categories and Krull–Schmidt partners”, Russian Math. Surveys, 71:3 (2016), 594–596  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. D. O. Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364  mathnet  crossref  scopus
    4. A. G. Kuznetsov, “Exceptional collections in surface-like categories”, Sb. Math., 208:9 (2017), 1368–1398  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. S. Gorchinskiy, “Integral Chow motives of threefolds with $K$-motives of unit type”, Bull. Korean. Math. Soc., 54:5 (2017), 1827–1849  crossref  mathscinet  isi  scopus
    6. P. Belmans, T. Raedschelders, “Embeddings of algebras in derived categories of surfaces”, Proc. Amer. Math. Soc., 145:7 (2017), 2757–2770  crossref  mathscinet  zmath  isi  scopus
    7. M. Kalck, “Derived categories of quasi-hereditary algebras and their derived composition series”, Representation Theory - Current Trends and Perspectives, EMS Ser. Congr. Rep., eds. H. Krause, P. Littelmann, G. Malle, K. H. Neeb, C. Schweigert, Eur. Math. Soc., 2017, 269–308  mathscinet  zmath  isi
    8. D. B. Kaledin, “Witt vectors, commutative and non-commutative”, Russian Math. Surveys, 73:1 (2018), 1–30  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. L. Chekhov, M. Mazzocco, “Colliding holes in Riemann surfaces and quantum cluster algebras”, Nonlinearity, 31:1 (2018), 54–107  crossref  mathscinet  zmath  isi  scopus
    10. P. Belmans, D. Presotto, “Construction of non-commutative surfaces with exceptional collections of length 4”, J. Lond. Math. Soc.-Second Ser., 98:1 (2018), 85–103  crossref  zmath  isi  scopus
    11. D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. E. Ballico, S. Barmeier, E. Gasparim, L. Grama, L. A. B. San Martin, “A Lie theoretical construction of a Landau-Ginzburg model without projective mirrors”, Manuscr. Math., 158:1-2 (2019), 85–101  crossref  mathscinet  zmath  isi
    13. P. Belmans, L. Fu, T. Raedschelders, “Hilbert squares: derived categories and deformations”, Sel. Math.-New Ser., 25:3 (2019), UNSP 37  crossref  isi
    14. D. Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096  crossref  mathscinet  isi
    15. P. Belmans, T. Raedschelders, “Derived categories of noncommutative quadrics and Hilbert squares”, Int. Math. Res. Notices, 2020:19 (2020), 6042–6069  crossref  mathscinet  isi
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