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Mathematics of the USSR-Izvestiya, 1990, Volume 34, Issue 1, Pages 23–42
DOI: https://doi.org/10.1070/IM1990v034n01ABEH000583
(Mi im1160)
 

This article is cited in 165 scientific papers (total in 165 papers)

Representation of associative algebras and coherent sheaves

A. I. Bondal
References:
Abstract: It is proved that a triangulated category generated by a strong exceptional collection is equivalent to the derived category of modules over an algebra of homomorphisms of this collection. For the category of coherent sheaves on a Fano variety, the functor of tightening to a canonical class is described by means of mutations of an exceptional collection generating the category. The connection between mutability of strong exceptional collections and the Koszul property is studied. It is proved that in the geometric situation mutations of exceptional sheaves consist of present sheaves and the corresponding algebra of homomorphisms is Koszul and selfconsistent.
Bibliography: 18 titles.
Received: 29.03.1988
Bibliographic databases:
Document Type: Article
UDC: 512
MSC: 16A46, 16A64, 18F20
Language: English
Original paper language: Russian
Citation: A. I. Bondal, “Representation of associative algebras and coherent sheaves”, Math. USSR-Izv., 34:1 (1990), 23–42
Citation in format AMSBIB
\Bibitem{Bon89}
\by A.~I.~Bondal
\paper Representation of associative algebras and coherent sheaves
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 23--42
\mathnet{http://mi.mathnet.ru/eng/im1160}
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000583}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=992977}
\zmath{https://zbmath.org/?q=an:0692.18002}
Linking options:
  • https://www.mathnet.ru/eng/im1160
  • https://doi.org/10.1070/IM1990v034n01ABEH000583
  • https://www.mathnet.ru/eng/im/v53/i1/p25
  • This publication is cited in the following 165 articles:
    1. Andreas Krug, Erik Nikolov, “Endomorphism Algebras of Equivariant Exceptional Collections”, Algebr Represent Theor, 2025  crossref
    2. M. V. Bondarko, “Producing new semi-orthogonal decompositions in arithmetic geometry”, Sb. Math., 215:4 (2024), 511–542  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Izzet Coskun, Jack Huizenga, Geoffrey Smith, “Stability and Cohomology of Kernel Bundles on Pn”, Michigan Math. J., -1:-1 (2024)  crossref
    4. Yu-Wei Fan, Junho Peter Whang, “Stokes matrices and exceptional isomorphisms”, Math. Ann., 2024  crossref
    5. Edson Ribeiro Alvares, Eduardo Nascimento Marcos, Hagen Meltzer, “On the Braid Group Action on Exceptional Sequences for Weighted Projective Lines”, Algebr Represent Theor, 27:1 (2024), 897  crossref
    6. Tomoki Yoshida, “Full exceptional collections of line bundles on the blow-up of P5 along Segre threefold”, manuscripta math., 2024  crossref
    7. Xiao-Wu Chen, Zhengfang Wang, “The singular Yoneda category and the stabilization functor”, Math. Z., 308:2 (2024)  crossref
    8. Russian Math. Surveys, 79:5 (2024), 807–845  mathnet  crossref  crossref  mathscinet  adsnasa
    9. L. Guseva, “On the Derived Category of the Cayley Grassmannian”, Math. Notes, 113:1 (2023), 149–153  mathnet  crossref  crossref  mathscinet
    10. A. V. Fonarev, “Dual exceptional collections on Lagrangian Grassmannians”, Sb. Math., 214:12 (2023), 1779–1800  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. Laura Pertusi, Paolo Stellari, “Categorical Torelli theorems: results and open problems”, Rend. Circ. Mat. Palermo, II. Ser, 72:5 (2023), 2949  crossref
    12. Emre Coskun, Ozhan Genc, “Ulrich trichotomy on del Pezzo surfaces”, Advances in Geometry, 23:1 (2023), 51  crossref
    13. Riccardo Moschetti, Marco Rampazzo, “Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold”, Algebr Represent Theor, 2023  crossref
    14. Wen Chang, Sibylle Schroll, “Exceptional sequences in the derived category of a gentle algebra”, Sel. Math. New Ser., 29:3 (2023)  crossref
    15. Laura Pertusi, Ethan Robinett, “Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor”, Mathematische Nachrichten, 296:7 (2023), 2975  crossref
    16. Patricio Gallardo, Benjamin Schmidt, “Variation of stability for moduli spaces of unordered points in the plane”, Trans. Amer. Math. Soc., 2023  crossref
    17. Dae-Won Lee, “Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two”, Advances in Geometry, 23:1 (2023), 25  crossref
    18. Elin Persson Westin, Markus Thuresson, “Tilting Modules and Exceptional Sequences for a Family of Dual Extension Algebras”, Algebr Represent Theor, 26:5 (2023), 1549  crossref
    19. Dmitrii Pirozhkov, “Rouquier dimension of some blow-ups”, Eur. J. Math., 9 (2023), 45–13  mathnet  crossref
    20. R. Bautista, E. Pérez, L. Salmerón, “Homological systems and bocses”, Journal of Algebra, 617 (2023), 192  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:3577
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    References:143
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