Mukai flops and derived categories II

Details Mukai flops and derived categories II Mukai flops and derived categories II

2003-05-06

arxiv.org/abs/math/0305086v2

Mathematics

Algebraic Geometry

30 pages An assumption of Theorem 2.7 is removed

Scientific paper

This paper is a sequel to math.AG/0203287. A generalization of the Mukai flop has been studied by E. Markman. Here we call it a stratified Mukai flop. In this paper, we observe that, for a stratified Mukai flop: $X \to \bar{X} \leftarrow X^+$, the fiber product $X \times_{\bar{X}}X^+$ defines an isomorphism of Grothendieck groups $K(X) \to K(X^+)$, but, at the level of derived categories, the fiber product does not generally give an equivalence.

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