Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties

@article{Li1996VirtualMC,
  title={Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties},
  author={J. Li and G. Tian},
  journal={Journal of the American Mathematical Society},
  year={1996},
  volume={11},
  pages={119-174}
}
  • J. Li, G. Tian
  • Published 1996
  • Mathematics
  • Journal of the American Mathematical Society
We introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex. We apply this method to constructing the virtual moduli cycle of the moduli of stable maps from n-pointed genus g curves to any smooth projective variety. As an application, we give an algebraic definition of GW-invariants for any smooth projective variety. 
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