Crepant resolution and the holomorphic anomaly equation for C^3/Z_3

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.

arXiv comment41 pages, typos corrected

References in corpus (18)

• A New Cohomology Theory for Orbifold
• The structure of 2D semi-simple field theories
• Orbifold Quantum Riemann-Roch, Lefschetz and Serre
• Equivariant Gromov - Witten Invariants
• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
• Semisimple Frobenius structures at higher genus
• Mirror Theorem for Elliptic Quasimap Invariants
• On the Crepant Resolution Conjecture in the Local Case
• On the mathematics and physics of high genus invariants of [C^3/Z_3]
• The orbifold quantum cohomology of C^2/Z_3 and Hurwitz-Hodge integrals
• Genus-One Mirror Symmetry in the Landau-Ginzburg Model
• Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture
• Hodge-Theoretic Mirror Symmetry for Toric Stacks
• Gromov-Witten Invariants of Local P^2 and Modular Forms
• Wall-Crossing in Genus Zero Landau-Ginzburg Theory
• Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves
• Orbifold quantum cohomology of the symmetric product of A_r

Cited by in corpus (6)

• Holomorphic anomaly equation for $({\mathbb{P}}^2,E)$ and the Nekrasov-Shatashvili limit of local ${\mathbb{P}}^2$
• Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
• Gromov-Witten invariants of Calabi-Yau fibrations
• Quasi-modularity and holomorphic anomaly equation for the twisted Gromov-Witten theory: $\mathcal{O}(3)$ over ${\mathbb{P}}^2$
• Higher Genus Gromov-Witten Theory of C^n/Z_n I: Holomorphic Anomaly Equations
• Holomorphic anomaly equations for ${\mathbb{C}}^5/{\mathbb{Z}}_5$