Smooth Morphisms of Module Schemes

Let :A to B be a homomorphism of finite-dimensional algebrasover an algebraically closed field and the induced morphism of the associated module schemesfor any integer c 1. We prove that if the induced functor modB mod A is hom-controlled then the restriction of ^(c) to anyconnected component of is a composition of a smooth morphism followed by an immersion.Some new results on the types of singularities in the orbitclosures of module schemes are also proved. 2000 Mathematical Subject Classification: 14B05, 14L30, 16G10.