We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n -f 1 folds X n+ i to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z n . The interpretation of these data as valid classical solutions of the heterotic string compactified on Z n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n + 1-fold X n +i a toric n fold Z n together with a specific family of sheaves on it. This allows for a systematic construction of phenomenologically interesting d = 4 N = 1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and 5(7(3) x 5(7(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.
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Berglund et al. (1998) studied this question.