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

Understand

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.