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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 290, Pages 80–94
DOI: https://doi.org/10.1134/S0371968515030073 (Mi tm3641)

This article is cited in 19 scientific papers (total in 19 papers)

Geometric realizations of quiver algebras

D. O. Orlov

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

Full-text PDF (265 kB) Citations (19)

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DOI: https://doi.org/10.1134/S0371968515030073

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.

Received: March 15, 2015

English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 290, Issue 1, Pages 70–83
DOI: https://doi.org/10.1134/S0081543815060073

Bibliographic databases:

Document Type: Article

UDC: 512.7

Language: Russian

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

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https://www.mathnet.ru/eng/tm3641

https://doi.org/10.1134/S0371968515030073

https://www.mathnet.ru/eng/tm/v290/p80

This publication is cited in the following 19 articles:

Fonarev A., “On the Bounded Derived Category of Igr(3,7)”, Transform. Groups, 27:1 (2022), 89–112
Lorenzin A., “Compatibility of T-Structures in a Semiorthogonal Decomposition”, Appl. Categ. Struct., 30:4 (2022), 755–778
Theo Raedschelders, Greg Stevenson, “Proper connective differential graded algebras and their geometric realizations”, European Journal of Mathematics, 8:S2 (2022), 574
Dimitrov G., Katzarkov L., “Noncommutative Counting Invariants and Curve Complexes”, Int. Math. Res. Notices, 2021, rnaa374
D. Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096
P. Belmans, T. Raedschelders, “Derived categories of noncommutative quadrics and Hilbert squares”, Int. Math. Res. Notices, 2020:19 (2020), 6042–6069
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
P. Belmans, L. Fu, T. Raedschelders, “Hilbert squares: derived categories and deformations”, Sel. Math.-New Ser., 25:3 (2019), UNSP 37
D. B. Kaledin, “Witt vectors, commutative and non-commutative”, Russian Math. Surveys, 73:1 (2018), 1–30
L. Chekhov, M. Mazzocco, “Colliding holes in Riemann surfaces and quantum cluster algebras”, Nonlinearity, 31:1 (2018), 54–107
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
D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918
Yijia Liu, Springer Proceedings in Mathematics & Statistics, 240, Superschool on Derived Categories and D-branes, 2018, 35
A. G. Kuznetsov, “Exceptional collections in surface-like categories”, Sb. Math., 208:9 (2017), 1368–1398
S. Gorchinskiy, “Integral Chow motives of threefolds with $K$ -motives of unit type”, Bull. Korean. Math. Soc., 54:5 (2017), 1827–1849
P. Belmans, T. Raedschelders, “Embeddings of algebras in derived categories of surfaces”, Proc. Amer. Math. Soc., 145:7 (2017), 2757–2770
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
D. O. Orlov, “Gluing of categories and Krull–Schmidt partners”, Russian Math. Surveys, 71:3 (2016), 594–596
D. O. Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364

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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