We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov-Witten invariants (g 5) of the derived equivalent Calabi-Yau 3-folds, which are of the appropriate codimensions in the Grassmannian Gr(2, 7) and the Pfaffian Pf(7).
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Hosono et al. (2009) studied this question.