Eyal Markman, University of Massachusetts Amherst

Flops and derived categories, after Tom Bridgeland

Let Y be a smooth projective threefold and E a smooth rational curve in Y. If the normal bundle of E is suitable, then E can be flopped to produce another birational model W of Y. Bridgeland describes W as a moduli space of objects in the derived category of Y, which he calls perverse coherent sheaves. He then proves that Y and W have equivalent derived categories. Chains of flops relate any two crepent resolutions Y, Y' of a complex projective threefold X with terminal singularities. Hence, Y and Y' have equivalent derived categories.

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