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

From: American Journal of Mathematics
Volume 131, Number 4, August 2009
pp. 1009-1046 | 10.1353/ajm.0.0063

Abstract

Abstract:

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~${\Bbb P}^1$.