D-branes on noncompact Calabi–Yau manifolds: K-theory and monodromy Original Research Article

We study D-branes on smooth noncompact toric Calabi–Yau manifolds that are resolutions of Abelian orbifold singularities. Such a space has a distinguished basis {Si} for the compactly supported K-theory. Using local mirror symmetry we demonstrate that the Si have simple transformation properties under monodromy; in particular, they are the objects that generate monodromy around the principal component of the discriminant locus. One of our examples, the toric resolution of C3/(Z2×Z2), is a three parameter model for which we are able to give an explicit solution of the GKZ system.