Weighted blowup correspondence of orbifold Gromov--Witten invariants and applications

Let $\mathsf{X}$ be a symplectic orbifold groupoid with $\mathsf{S}$ being a symplectic sub-orbifold groupoid, and ${\mathsf{X}}_{\mathfrak{a}}$ be the weight-$\mathfrak{a}$ blowup of $\mathsf{X}$ along $\mathsf{S}$ with $\mathsf{Z}$ being the corresponding exceptional divisor. We show that there is a weighted blowup correspondence between some certain absolute orbifold Gromov–Witten invariants of $\mathsf{X}$ relative to $\mathsf{S}$ and some certain relative orbifold Gromov–Witten invariants of the pair $({\mathsf{X}}_{\mathfrak{a}}\mathsf{\mid }\mathsf{Z})$. As an application, we prove that the symplectic uniruledness of symplectic orbifold groupoids is a weighted blowup invariant.