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arXiv · 0804.3144

Singular symplectic flops and Ruan cohomology

Bohui Chen·An-Min Li·Qi Zhang·Guosong Zhao
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Abstract

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/μ_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let $X$ and $Y$ be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of exceptional classes on $X$ and $Y$ and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.

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Bohui Chen, An-Min Li, Qi Zhang, Guosong Zhao. 2008-04-19. Singular symplectic flops and Ruan cohomology. https://arxiv.org/abs/0804.3144

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