2024/03/25 by Wang, Yu, You, Fenglong
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.17200
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 \mathbb P1-bundle P:=\mathbb P(\mathcal OX(-D)⊕ \mathcal 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.