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

TL;DR

This paper establishes a correspondence between orbifold Gromov--Witten invariants under weighted blowups of symplectic orbifold groupoids, demonstrating that symplectic uniruledness remains invariant under such transformations.

Contribution

It introduces a weighted blowup correspondence for orbifold Gromov--Witten invariants and applies it to prove uniruledness invariance under weighted blowups.

Findings

Weighted blowup correspondence between absolute and relative orbifold Gromov--Witten invariants.

Symplectic uniruledness is preserved under weighted blowups.

New tools for studying orbifold Gromov--Witten invariants in symplectic geometry.

Abstract

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