## Geometry & Topology

### Orbifold Gromov–Witten theory of the symmetric product of $\mathcal{A}_r$

#### Abstract

Let $Ar$ be the minimal resolution of the type $Ar$ surface singularity. We study the equivariant orbifold Gromov–Witten theory of the $n$–fold symmetric product stack $[Symn(Ar)]$ of $Ar$. 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 $Symn(Ar)$ is valid. More strikingly, we complete a tetrahedron of equivalences relating the Gromov–Witten theories of $[Symn(Ar)]∕Hilbn(Ar)$ and the relative Gromov–Witten/Donaldson–Thomas theories of $Ar×ℙ1$.

#### Article information

Source
Geom. Topol., Volume 16, Number 1 (2012), 475-526.

Dates
Revised: 3 September 2011
Accepted: 15 November 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732387

Digital Object Identifier
doi:10.2140/gt.2012.16.475

Mathematical Reviews number (MathSciNet)
MR2916292

Zentralblatt MATH identifier
1245.14055

#### Citation

Cheong, Wan Keng; Gholampour, Amin. Orbifold Gromov–Witten theory of the symmetric product of $\mathcal{A}_r$. Geom. Topol. 16 (2012), no. 1, 475--526. doi:10.2140/gt.2012.16.475. https://projecteuclid.org/euclid.gt/1513732387

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