ar X iv : m at h / 02 07 17 0 v 1 [ m at h . A G ] 1 9 Ju l 2 00 2 THREE - DIMENSIONAL FLOPS AND NON - COMMUTATIVE RINGS MICHEL
نویسنده
چکیده
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 Bridge-land. 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 ").
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