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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 alsodoi:10.1007/jhep04(2020)203 fatcat:3qcpza2m4raezfey5tiqkuhps4