Toric Resolutions of Heterotic Orbifolds

We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of C^n/Z_n singularities. We show that the values of the relevant integrals, computed there, can be obtained as integrals of divisors (complex codimension one hypersurfaces) interpreted as (1,1)-forms in toric geometry. Motivated by this we give a self contained introduction to toric geometry for non-experts, focusing on those issues relevant for the construction of heterotic models on toric orbifold resolutions. We illustrate the methods by building heterotic models on the resolutions of C^2/Z_3, C^3/Z_4 and C^3/Z_2xZ_2'. We are able to obtain a direct identification between them and the known orbifold models. In the C^3/Z_2xZ_2' case we observe that, in spite of the existence of two inequivalent resolutions, fully consistent blowup models of heterotic orbifolds can only be constructed on one of them.