Dieterich, Ernst The Auslander-Reiten quiver of an isolated singularity. (English) Zbl 0632.14004 Singularities, representation of algebras, and vector bundles, Proc. Symp., Lambrecht/Pfalz/FRG 1985, Lect. Notes Math. 1273, 244-264 (1987). [For the entire collection see Zbl 0619.00007.] In the first part of the paper the theory of almost split sequences of Auslander-Reiten is reviewed for the category of maximal Cohen-Macaulay modules over the local ring of the singularity of an algebraic variety. The second part deals with the question of existence of a reduction ideal and consequences thereof, in particular “Brauer-Thrall I” for affine algebraic isolated Cohen-Macaulay singularities. Details of the proofs appeared in the author’s paper in Comment. Math. Helv. 62, 654-676 (1987). Reviewer: H.Knörrer Cited in 1 ReviewCited in 5 Documents MSC: 14B05 Singularities in algebraic geometry 16Gxx Representation theory of associative rings and algebras 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) Keywords:Auslander-Reiten-quivers; Brauer-Thrall conjecture; maximal Cohen- Macaulay modules; local ring of the singularity Citations:Zbl 0619.00007 PDFBibTeX XML