Abstract
In this paper, we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities, $$V_{r,b} = \{ (x,y,z,t) \in \mathbb{C}^4 |xy - z^{2r} + t^2 = 0\} /\mu _r (a, - a,b,0),r \geqslant 2,$$ where b = 1 appears in Mori’s minimal model program and b ≠ 1 is a new class of singularities in symplectic birational geometry. We prove that two symplectic 3-orbifolds which are singular flops to each other have isomorphic Ruan cohomology rings. The proof is based on the symplectic cutting argument and virtual localization technique.
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