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Three-dimensional flops and noncommutative rings
Michel Van den Bergh
Source: Duke Math. J. Volume 122, Number 3
(2004), 423-455.
Abstract
For $Y,Y^+$ three-dimensional smooth varieties related by a flop, Bondal and Orlov conjectured that the derived categories $D^b(\coh(Y))$ and $D^b(\coh(Y^+))$ are equivalent. This conjecture was recently proved by Bridgeland. Our aim in this paper is to give a partially new proof of Bridgeland's result using noncommutative rings. The new proof also covers some mild singular and higher-dimensional situations (including those occuring in the recent paper by Chen [11]).
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1082665284
Digital Object Identifier: doi:10.1215/S0012-7094-04-12231-6
Mathematical Reviews number (MathSciNet): MR2057015
Zentralblatt MATH identifier: 02133073
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