D-Branes on Noncompact Calabi-Yau Manifolds: K-Theory and Monodromy

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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 x Z_2), is a three parameter model for which we are able to give an explicit solution of the GKZ system.

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