Smooth Morphisms of Module Schemes

Let φ: A to B be a homomorphism of finite‐dimensional algebras over an algebraically closed field and φ ( c ) : m o d B c → m o d A c the induced morphism of the associated module schemes for any integer c ⩾ 1. We prove that if the induced functor mod B → mod A is hom‐controlled then the restriction of φ (c) to any connected component ofm o d B c is a composition of a smooth morphism followed by an immersion. Some new results on the types of singularities in the orbit closures of module schemes are also proved. 2000 Mathematical Subject Classification : 14B05, 14L30, 16G10.