Gerby localization, ℤ₃-Hodge integrals and the GW theory of [ℂ³/ℤ₃]


We exhibit a set of recursive relations that completely determine all equivariant Gromov-Witten invariants of $[{\Bbb C}^3/{\Bbb Z}_3]$. We interpret such invariants as ${\Bbb Z}_3$-Hodge integrals, and produce relations among them via Atiyah-Bott localization on moduli spaces of twisted stable maps to gerbes over~${\Bbb P}^1$.