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arXiv · 0707.1337

Root Systems and the Quantum Cohomology of ADE resolutions

Jim Bryan·Amin Gholampour
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Abstract

We compute the C*-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C^2/G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n 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 [C^2/G].

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Jim Bryan, Amin Gholampour. 2007-07-09. Root Systems and the Quantum Cohomology of ADE resolutions. https://arxiv.org/abs/0707.1337

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