Mukai flops and derived categories II

Abstract

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.

30 pages An assumption of Theorem 2.7 is removed