  The geometric small property (Borho-MacPherson) of projective morphisms
implies a description of their singularities in terms of intersection homology.
In this paper we solve the smallness problem raised by Nakajima
(math.QA/0105173) for certain resolutions of quiver varieties (analogs of the
Springer resolution) : for Kirillov-Reshetikhin modules of simply-laced quantum
affine algebras, we characterize explicitly the Drinfeld polynomials
corresponding to the small resolutions. We use an elimination theorem for
monomials of Frenkel-Reshetikhin q-characters that we establish for non
necessarily simply-laced quantum affine algebras. We also refine results of
(math.QA/0501202) and extend the main result to general simply-laced quantum
affinizations, in particular to quantum toroidal algebras (double affine
quantum algebras).
