Singular symplectic flops and Ruan cohomology

Bohui Chen; An-Min Li; Qi Zhang; Guosong Zhao

paper

Singular symplectic flops and Ruan cohomology

arXiv:0804.3144

Abstract

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $W_{r} = {(x, y, z, t) ∣ x y - z^{2 r} + t^{2} = 0} / μ_{r} (a, - a, 1, 0), r \geq 1,$ 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.

34pages