D-branes on a Noncompact Singular Calabi-Yau Manifold
  We investigate D-branes on a noncompact singular Calabi-Yau manifold by using the boundary CFT description, and calculate the open string Witten indices between the boundary states. The B-type D-branes turn out to be characterized by the properties of a compact positively curved manifold. We give geometric interpretations to these boundary states in terms of coherent sheaves of the manifold. 
Katsuyuki Sugiyama and Satoshi Yamaguchi (Kyoto Univ.)