As was mentioned above, many moduli spaces have a quiver description; one of the most famous example is given by Nakajima quiver varieties, which are defined for any quiver (and they serve as the main example of symplectic complex varieties which are resolutions of an affine variety), but when the quiver is the affine quiver of ADE type, they describe moduli spaces of torsion free sheaves on the quotients of ${\mathbb C}^2/\Gamma$ where $\Gamma$ is a finite subgroup of $SL(2)$ (these are also known as ALE spaces). These moduli spaces are very important in many places in mathematics and physics (gauge theory) and quiver description is very useful when you want to tackle some explicit problems related to them.
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As was mentioned above, many moduli spaces have a quiver description; one of the most famous example is given by Nakajima quiver varieties, which are defined for any quiver (and they serve as the main example of symplectic complex varieties which are resolutions of an affine variety), but when the quiver is the affine quiver of ADE type, they describe moduli spaces of torsion free sheaves on quotients of ${\mathbb C}^2/\Gamma$ where $\Gamma$ is a finite subgroup of $SL(2)$ (these are also known as ALE spaces). These moduli spaces are very important in many places in mathematics and physics (gauge theory) and quiver description is very useful when you want to tackle some explicit problems related to them. |
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