Proves quasi-modularity and derives holomorphic anomaly equation for twisted GW theory of O(3) over P².
Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
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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 CP2. The proof of the correspondence requires an identity proven in the Appendix by T. Coates and H. Iritani.
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Quasi-modularity and holomorphic anomaly equation for the twisted Gromov-Witten theory: $\mathcal{O}(3)$ over $\mathbb{P}^2$
Proves quasi-modularity and derives holomorphic anomaly equation for twisted GW theory of O(3) over P².