Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3

Abstract

We exhibit a set of recursive relations that completely determine all equivariant Gromov-Witten invariants of the quotient orbifold C^3/Z_3. We interpret such invariants as G-Hodge Integrals, and produce relations among them via Atiyah-Bott localization on moduli spaces of twisted stable maps to gerbes over the projective line.

Added a section with system of PDE's encoding the recursions

References in corpus (5)

• Introduction to the language of stacks and gerbes
• The Crepant Resolution Conjecture for Type A Surface Singularities
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Generating Functions for Hurwitz-Hodge Integrals
• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves

Cited by in corpus (4)

• Equivariant Gromov-Witten theory of one dimensional stacks
• Crepant resolution conjecture in all genera for type A singularities
• On computations of Hurwitz-Hodge integrals
• Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples