Abstract
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 local P 2 . The proof of the correspondence requires an identity proven in the Appendix by T. Coates and H. Iritani.
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