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 relative/orbifold Gromov--Witten invariants of a P¹-bundle P: = P (OX (-D) OX) with n relative markings. This is a generalization of the local-relative correspondence beyond maximal contacts. Repeating this process, we identify genus zero relative Gromov--Witten invariants 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.