Gromov--Witten theory beyond maximal contacts

Given a smooth projective variety $X$ and a smooth nef divisor $D$, we identify genus zero relative Gromov–Witten invariants of $(X,D)$ with $(n+1)$ relative markings with genus zero orbifold Gromov–Witten invariants of multi-root stacks over the ${\mathbb{P}}^1$-bundle $P:=\mathbb{P}({\mathcal{O}}_X(-D)\oplus {\mathcal{O}}_X)$ with $n$ orbifold markings. This is a generalization of the local-relative correspondence beyond maximal contacts. Repeating this process, we identify genus zero relative Gromov–Witten invariants of ambient insertions with genus zero absolute Gromov–Witten invariants of toric bundles. We also present how this correspondence can be used to compute genus zero two-point relative Gromov–Witten invariants.