The Auslander-Reiten quiver of a simple curve singularity

Abstract

With any simple curve singularity (plane, complex, affine-algebraic) of Dynkin-type Δ \Delta we associate the category of all finitely generated torsionfree modules over its complete local ring. For each of these module categories we calculate the Auslander-Reiten quiver. We suggest the construction of the “twisted quiver” of a quiver with involution and valuation of arrows which gives rise to a (purely combinatorial) one-to-one correspondence between the Auslander-Reiten quiver and the Dynkin diagram Δ \Delta .