On degenerations and extensions of finite dimensional modules. (English) Zbl 0862.16007
The paper deals with a geometric study of finite dimensional modules over a finite dimensional associative algebra. The author proves a cancellation theorem for degenerations of modules and considers its applications to the theory of preprojective modules and modules over tame concealed algebras, the theory of matrix pencils and others. In fact, the main results of the article under review have been improved and generalized in two papers written later but published earlier [K. Bongartz, Comment. Math. Helv. 69, No. 4, 575-611 (1994; Zbl 0832.16008) and Ann. Sci. Éc. Norm. Supér., IV. Sér. 28, No. 5, 647-668 (1995; Zbl 0844.16007)].
Reviewer: A.G.Aleksandrov (Moskva)
MSC:
| 16G20 | Representations of quivers and partially ordered sets |
| 16P10 | Finite rings and finite-dimensional associative algebras |
| 16G60 | Representation type (finite, tame, wild, etc.) of associative algebras |
| 14L30 | Group actions on varieties or schemes (quotients) |
| 16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
| 14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
| 14B05 | Singularities in algebraic geometry |
| 16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
