Quantum invariance under $\mathbb{P}^1$ flops of type $(k + 2, k)$

Abstract

In the joint paper [8] with Y.-P. Lee and C.-L. Wang, we have shown that the big quantum ring is invariant under $\mathbb{P}^r$ flops of splitting type, after an analytic continuation over the extended Kähler moduli space. It is a generalization of our previous work for the case of simple $\mathbb{P}^r$ flops [7]. In this note, I would like to outline the results and concentrate mainly on the detailed study of a simple type, called $\mathbb{P}^1$ flops of type $(k + 2, k)$.