New proof demonstrates equivalence of derived categories in three-dimensional smooth varieties, indicating broader applicability in singular cases.
For Y,Y⁺ three-dimensional smooth varieties related by a flop, Bondal and Orlov conjectured that the derived categories Dᵇ( coh(Y)) and Dᵇ( 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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Michel Van den Bergh (2004) studied this question.
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