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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 1, Pages 25–44 (Mi izv1160)  

This article is cited in 88 scientific papers (total in 88 papers)

Representation of associative algebras and coherent sheaves

A. I. Bondal


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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:1, 23–42

Bibliographic databases:

Document Type: Article
UDC: 512
MSC: 16A46, 16A64, 18F20
Received: 29.03.1988

Citation: A. I. Bondal, “Representation of associative algebras and coherent sheaves”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989), 25–44; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 1
\pages 25--44
\mathnet{http://mi.mathnet.ru/izv1160}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=992977}
\zmath{https://zbmath.org/?q=an:0692.18002}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 23--42
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000583}


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    This publication is cited in the following articles:
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