Three-dimensional flops and non-commutative rings

Research output: Contribution to journalArticle


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 non-commutative rings. The new proof also covers some mild singular and higher dimensional situations (including the one in the recent paper by Chen: ``Flops and Equivalences of derived Categories for Threefolds with only Gorenstein Singularities'').
Original languageEnglish
Pages (from-to)423-455
Number of pages33
JournalDuke Mathematical Journal
Publication statusPublished - 2004


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