Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 4 (2008), 369-390.
Root systems and the quantum cohomology of ADE resolutions
We compute the -equivariant quantum cohomology ring of , the minimal resolution of the DuVal singularity where is a finite subgroup of . The quantum product is expressed in terms of an ADE root system canonically associated to . We generalize the resulting Frobenius manifold to nonsimply laced root systems to obtain an parameter family of algebra structures on the affine root lattice of any root system. Using the Crepant Resolution Conjecture, we obtain a prediction for the orbifold Gromov–Witten potential of .
Algebra Number Theory, Volume 2, Number 4 (2008), 369-390.
Received: 10 August 2007
Revised: 9 May 2008
Accepted: 9 May 2008
First available in Project Euclid: 20 December 2017
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Bryan, Jim; Gholampour, Amin. Root systems and the quantum cohomology of ADE resolutions. Algebra Number Theory 2 (2008), no. 4, 369--390. doi:10.2140/ant.2008.2.369. https://projecteuclid.org/euclid.ant/1513797266