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'').
|Number of pages||33|
|Journal||Duke Mathematical Journal|
|Publication status||Published - 2004|