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

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

2007-09-24

arxiv.org/abs/0709.3805v1

Adv. Theor. Math. Phys. Vol. 13, No.3:695-719, 2009

Mathematics

Algebraic Geometry

17 pages, 2 figures

Scientific paper

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.

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