## Abstract

Let A _{r} be the minimal resolution of the type A _{r} surface singularity. We study the equivariant orbifold Gromov-Witten theory of the n-fold symmetric product stack [Sym ^{n}(A _{r})] of A _{r}. We calculate the divisor operators, which turn out to determine the entire theory under a nondegeneracy hypothesis. This, together with the results of Maulik and Oblomkov, shows that the Crepant Resolution Conjecture for Sym ^{n}(A _{r}) is valid. More strikingly, we complete a tetrahedron of equivalences relating the Gromov-Witten theories of [Sym ^{n}(A _{r})]/Hilb ^{n}(A _{r}) and the relative Gromov-Witten/Donaldson-Thomas theories of A _{r} × P ^{1}.

Original language | English |
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Pages (from-to) | 475-527 |

Number of pages | 53 |

Journal | Geometry and Topology |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Mar 29 |

## All Science Journal Classification (ASJC) codes

- Geometry and Topology