Three-dimensional flops and non-commutative rings

Details Three-dimensional flops and non-commutative rings Three-dimensional flops and non-commutative rings

2002-07-19

arxiv.org/abs/math/0207170v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

If Y,Z are three-dimensional smooth varieties related by a flop, then Bondal and Orlov conjectured that the derived categories of coherent sheaves on Y and Z 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'').

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