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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

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)

Citations:

Zbl 0619.00007