Orbifold quantum cohomology of the symmetric product of Ar
نویسنده
چکیده
Let Ar be the minimal resolution of the type Ar surface singularity. We study the equivariant quantum cohomology ring of the n-fold symmetric product stack [Sym(Ar)] of Ar. We calculate the operators of quantum multiplication by divisor classes. Under the assumption of the nonderogatory conjecture, these operators completely determine the ring structure, which gives an affirmative answer to the Crepant Resolution Conjecture on [Sym(Ar)] and Hilb(Ar). More strikingly, this allows us to complete a tetrahedron of equivalences relating the Gromov-Witten theories of [Sym(Ar)]/Hilb(Ar) and the relative Gromov-Witten/Donaldson-Thomas theories of Ar × P.
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