# are quiver varieties local complete intersections?

Is it known when a Nakajima quiver variety happens to be a local complete intersection?

[For simplicity consider an affine quiver variety, i.e. the categorical quotient of the zero set of the moment map on the space of representations of a doubled quiver]

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EDIT: Perhaps I should expand on this a little bit. In order for a conic symplectic singularity like an affine quiver variety to be an lci, any deformation of it must be lci as well. The deformation theory of conic affine symplectic varieties is very nice; there is a universal deformation (amongst those keeping the symplectic structure!) whose base is a vector space, and there are certain walls, which are codimension 1 pieces of the locus where the deformation is not Q-factorial and terminal (in most cases, this is means smooth, but not always). In essence the badness'' at these points is controlled by a single slice singularity. If for any of the walls, this singularity is not an lci, you're out of luck.