The Gromov-Witten invariants of symplectic manifolds

Details The Gromov-Witten invariants of symplectic manifolds The Gromov-Witten invariants of symplectic manifolds

2000-06-21

arxiv.org/abs/math/0006156v1

Mathematics

Algebraic Geometry

LaTeX, 75 pages. Version as of November 1999

Scientific paper

We study the fix point components of the big torus action on the moduli space of stable maps into a smooth projective toric variety, and apply Graber and Pandharipande's localization formula for the virtual fundamental class to obtain an explicit formula for the Gromov-Witten invariants of toric varieties. Using this formula we compute all genus-0 3-point invariants of the Fano manifold $\P(\O_{\P^2}(2) \oplus 1)$, and we show for the (non-Fano) manifold $\P(\O_{\P^2}(3) \oplus 1)$ that its quantum cohomology ring does not correspond to Batyrev's ring defined in \cite{bat93}.

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