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

Abstract 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 { S i } for the compactly supported K-theory. Using local mirror symmetry we demonstrate that the S i 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 C 3 /( Z 2 × Z 2 ) , is a three parameter model for which we are able to give an explicit solution of the GKZ system.