Determination of Gromov–Witten invariants after blowing up a curve

Let $Y$ be the blow-up of a smooth projective threefold $X$ along a curve $C$ such that $g(C)\geq 1$, or $g(C)=0$ and $-K_X.C\geq 0$. The associativity equations of the quantum product should suffice to determine all genus-$0$ Gromov–Witten invariants of $Y$ in terms of those of $X$. This concerns the reconstruction of quantum cohomological data under blow-ups along curves; the parser supplies no evidence that the claim has been resolved.