Example
Let X be the complex projective plane with its standard symplectic form (corresponding to the Fubini-Study metric) and complex structure. Let be the Poincaré dual of a line L. Then
The only nonzero Gromov-Witten invariants are those of class A = 0 or A = L. It turns out that
and
where δ is the Kronecker delta. Therefore
In this case it is convenient to rename as q and use the simpler coefficient ring Z. This q is of degree . Then
Read more about this topic: Quantum Cohomology
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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