TY - JOUR
T1 - Orbifold Gromov-Witten theory of the symmetric product of A r
AU - Cheong, Wan Keng
AU - Gholampour, Amin
PY - 2012/3/29
Y1 - 2012/3/29
N2 - 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.
AB - 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.
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U2 - 10.2140/gt.2012.16.475
DO - 10.2140/gt.2012.16.475
M3 - Article
AN - SCOPUS:84859418820
SN - 1465-3060
VL - 16
SP - 475
EP - 527
JO - Geometry and Topology
JF - Geometry and Topology
IS - 1
ER -