Localization of virtual classes

@article{Graber1997LocalizationOV,
  title={Localization of virtual classes},
  author={Tom Graber and Rahul Pandharipande},
  journal={Inventiones mathematicae},
  year={1997},
  volume={135},
  pages={487-518}
}
We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves (generalizing Kontsevich's genus 0 formulas). Also, excess integrals over spaces of higher genus multiple covers are computed. 
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