Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

We present a simple unified formula expressing the denominators of normalized R-matrices between fundamental modules over quantum loop algebras type ADE. It has an interpretation in terms representations Dynkin quivers and can be proved way using geometry graded quiver varieties. As by-product, we obtain geometric Kang-Kashiwara-Kim's generalized affine Schur-Weyl duality functor when it arises from family modules. also study several cases varieties are isomorphic to nilpotent orbits A.