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Smooth Morphisms of Module Schemes
Author(s) -
Zwara G.
Publication year - 2002
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013382
Subject(s) - mathematics , morphism , algebraically closed field , functor , homomorphism , mod , integer (computer science) , gravitational singularity , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , computer science , programming language
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.