The classification of special Cohen–Macaulay modules

By Osamu Iyama, M. Wemyss. 2008

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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.

View Paper: https://www.semanticscholar.org/paper/db3b9ab881c65757c79f42ffa154a1b5721abdb4

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Citations in the corpus

• On the Defect Group of a 6D SCFT (2015, unknown): “[59–61]): p q = (n− 1)− 1 m1 − 1 m2−.”
• On the classification of 6D SCFTs and generalized ADE orbifolds (2013, background): “The group actions and resolutions for D-type theories can be found for example in reference [39].”
• Flops and clusters in the homological minimal model programme (2014, methodology): “This then allows us to obtain the numbersb j usingAuslander– Reiten (=AR) theory, using the knitting–type constructions on the known AR quivers, as in [22].”