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DG categories and exceptional collections


Author: Agnieszka Bodzenta
Journal: Proc. Amer. Math. Soc. 143 (2015), 1909-1923
MSC (2010): Primary 14F05, 14J26
DOI: https://doi.org/10.1090/S0002-9939-2014-12420-8
Published electronically: December 19, 2014
MathSciNet review: 3314101
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Abstract: A description of how to assign to a full exceptional collection on a variety $ X$ a DG category $ \mathcal {C}$ such that the bounded derived category of coherent sheaves on $ X$ is equivalent to the bounded derived category of $ \mathcal {C}$ is given in a 1990 work by Bondal and Kapranov, Framed triangulated categories. In this paper we show that the category $ \mathcal {C}$ can be chosen to have finite-dimensional spaces of morphisms. We describe how it behaves under mutations and present an algorithm allowing us to calculate it for full exceptional collections with vanishing Ext$ ^k$ groups for $ k>1$.


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Additional Information

Agnieszka Bodzenta
Affiliation: Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Address at time of publication: National Research University Higher School of Economics, Department of Mathematics, 20 Myasnitskaya St, Moscow 101000 Russia
Email: a.bodzenta@mimuw.edu.pl, abodzenta@hse.ru

DOI: https://doi.org/10.1090/S0002-9939-2014-12420-8
Received by editor(s): August 2, 2012
Received by editor(s) in revised form: October 19, 2013
Published electronically: December 19, 2014
Additional Notes: The author was partially supported by MNiSW grant number NN 201 420639
Communicated by: Harm Derksen
Article copyright: © Copyright 2014 American Mathematical Society

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