In this paper we study compactifications of the N = 2 heterotic E 8 × E 8 string on (K3 × T 2 )/Z 3 with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that arise from one-loop amplitudes. We then identify candidates for dual type IIA compactifications on Calabi-Yau threefolds and compare the heterotic results with the corresponding topological string amplitudes. We find that the dual Calabi-Yau geometries are K3 fibrations that are also

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... nus one fibered with threesections. Moreover, we show that the intersection form on the polarization lattice of the K3 fibration has to be three times the intersection form on the Narain lattice Γ 1,1 .