Abstract
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 .
Citation
Jim Bryan. Amin Gholampour. "Root systems and the quantum cohomology of ADE resolutions." Algebra Number Theory 2 (4) 369 - 390, 2008. https://doi.org/10.2140/ant.2008.2.369
Information