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The Gromov-Witten class and a perturbation theory in algebraic geometry
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 123, Number 2, April 2001
- pp. 343-381
- 10.1353/ajm.2001.0013
- Article
- Additional Information
We propose a method to construct the virtual fundamental class based on the "Kontsevich principle," i.e., we formulate the notion of quasi manifold structrue and establish a way to obtain the fundamental class from it. Also, we show that there is a natural quasi manifold structure on the moduli stack of stable maps, and thus we arrive at the new construction of the Gromov-Witten class. We also prove the fixed point formula for our Gromov-Witten class.