  We show that Auslander algebras have a unique tilting and cotilting module
which is generated and cogenerated by a projective-injective; its endomorphism
ring is called the projective quotient algebra. For any representation-finite
algebra, we use the projective quotient algebra to construct desingularizations
of quiver Grassmannians, orbit closures in representation varieties, and their
desingularizations. This generalizes results of Cerulli Irelli, Feigin and
Reineke.
