The Classification of Special Cohen-Macaulay Modules

Abstract

In this paper we completely classify all the special Cohen-Macaulay (=CM) modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities. In every case we exhibit the specials explicitly in a combinatorial way. Our result relies on realizing the specials as those CM modules whose first Ext group vanishes against the ring R, thus reducing the problem to combinatorics on the AR quiver; such possible AR quivers were classified by Auslander and Reiten. We also give some general homological properties of the special CM modules and their corresponding reconstruction algebras.

36 pages, minor revision, to appear in Math. Z

References in corpus (2)

• The GL(2) McKay Correspondence
• The Special McKay correspondence as an equivalence of derived categories

Cited by in corpus (5)

• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• On the Defect Group of a 6D SCFT
• The GL(2) McKay Correspondence
• G-graphs and special representations for binary dihedral groups in GL(2,C)
• A New Triangulated Category for Rational Surface Singularities