Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
Hyenho Lho, Rahul Pandharipande
TL;DR
This paper proves the holomorphic anomaly equations for the orbifold Gromov-Witten theory of C^3/Z_3 and establishes an exact crepant resolution correspondence with local CP2, connecting orbifold and smooth geometries.
Contribution
It provides a rigorous proof of the holomorphic anomaly equations and establishes a precise crepant resolution correspondence for C^3/Z_3.
Findings
Holomorphic anomaly equations confirmed for C^3/Z_3
Exact crepant resolution correspondence established
Identity proven linking orbifold and resolved theories
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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