This question is related with my previous one Quantum cohomology rings as invariants, but now, I want to ask a more concrete thing. If $X$ and $Y$ are Poisson varieties which are isomorphic (as a Poisson varieties) then, Are their quantum cohomology rings isomorphic?
Thanks Tim. Actually, I was thinking in $X$ and $Y$ as symplectic varieties, I mean, as two Poisson varieties which are symplectic. In this case if the varieties are isomorphic as symplectic varieties their quantum cohomology rings are isomorphic. My question was really stupid. I apologise for that. Please, close it.