  This is an expository article on the singularities of nilpotent orbit
closures in simple Lie algebras over the complex numbers. It is slanted towards
aspects that are relevant for representation theory, including Maffei's theorem
relating Slodowy slices to Nakajima quiver varieties in type A. There is one
new observation: the results of Juteau and Mautner, combined with Maffei's
theorem, give a geometric proof of a result on decomposition numbers of Schur
algebras due to Fang, Henke and Koenig.
