Title : Sheaves on ALE spaces and quiver varieties
Abstract :
The space of the stability parameters, used to define a quiver
variety, has a chamber structure. For an affine type, there is a
distinguished chamber $C_0$ where the corresponding quiver variety is
the framed moduli space of $\Gamma$-equivariant torsion free sheaves
on $\mathbb C^2$. Here $\Gamma$ is the finite subgroup of
$SL_2(\mathbb C)$ corresponding to the affine quiver via the McKay
correspondence.
There is also another chamber $C_\infty$, most far
way from $C_0$, where the corresponding quiver variety is a framed
moduli space of torsion free sheaves on the ALE space, the minimal
resolution of $\mathbb C^2/\Gamma$. This result is an analog of a
similar identification for a framed moduli space of anti-self-dual
connections on an ALE space, given by Kronheimer and the author in 1989.