Abstract |
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We compute the C*-equivariant quantum cohomology ring
of Y , the minimal resolution of the
DuVal singularity C2 ∕ 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 nonsimply laced root systems to obtain an
n parameter family of algebra
structures on the afine root lattice of any root system.
Using the Crepant Resolution Conjecture, we obtain a prediction
for the orbifold Gromov–Witten potential of [C2 ∕ G].
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Keywords
quantum cohomology, root system, ADE
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Mathematical Subject Classification
Primary: 14N35
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Authors
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