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Description

Consider varieties X and X^+ related by flopping contractions f: X \to Y, f^+: X^+ \to Y with fibers of dimension less than or equal to one. The null category for f is the category of sheaves on X with vanishing derived direct image. I will show that the derived categories of null categories for f and f^+ form a spherical pair in an appropriate quotient of the derived category of the fiber product of X and X^+ over Y. The associated auto-equivalence of the derived category of X is the flop-flop functor. This is a joint work with A. Bondal.