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Gerby localization, ℤ₃-Hodge integrals and the GW theory of [ℂ³/ℤ₃]
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 4, August 2009
- pp. 1009-1046
- 10.1353/ajm.0.0063
- Article
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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~${\Bbb P}^1$.
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