Orbifold Gromov-Witten theory of the symmetric product of A r

Wan Keng Cheong, Amin Gholampour

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)475-527
Number of pages53
JournalGeometry and Topology
Issue number1
Publication statusPublished - 2012 Mar 29

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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