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We study the orbifold Gromov–Witten theory of the quotient    [    C   3   /   Z  3   ]    in all genera. Our first result is a proof of the holomorphic anomaly equations in the precise form predicted by   B  ‐model physics. Our second result is an exact crepant resolution correspondence relating the Gromov–Witten theories of    [    C   3   /   Z  3   ]    and localP   2   . The proof of the correspondence requires an identity proven in the Appendix by T. Coates and H. Iritani.

Crepant resolution and the holomorphic anomaly equation for [ C 3 / Z 3 ]