On the mathematics and physics of high genus invariants of [C^3/Z_3]

Abstract

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [arXiv:hep-th/0607100] that predicts Gromov-Witten invariants of [C^3/Z_3] in arbitrary genus, and of the mathematical framework for expressing these invariants as Hodge integrals. Using geometric properties of the Hodge classes, we compute the unpointed invariants for g=2,3, thus providing the first high genus mathematical check of the physics predictions.

17 pages, 2 figures

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• The Crepant Resolution Conjecture for Type A Surface Singularities
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• Root Systems and the Quantum Cohomology of ADE resolutions
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Cited by in corpus (10)

• The Omega deformed B-model for rigid N=2 theories
• Global Properties of Topological String Amplitudes and Orbifold Invariants
• Crepant resolution conjecture in all genera for type A singularities
• On computations of Hurwitz-Hodge integrals
• Gromov-Witten Invariants of Local P^2 and Modular Forms
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle
• The Physical Mirror Equivalence for the Local P^2
• D-Branes on C^3_6 part I: prepotential and GW-invariants
• Virasoro constraints and descendant Hurwitz-Hodge Integrals