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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology