Examples of degenerations of Cohen-Macaulay modules

2010/12/24 by Hiramatsu, Naoya, Yoshino, Yuji
#16G50 #16G60 #16G70 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13C14 #Rings and Algebras (math.RA) #Secondary 13D10

paper · doi:10.48550/arxiv.1012.5346

Abstract

We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional simple hypersurface singularity of type (A_n) are given by extensions. We also prove that all extended degenerations of maximal Cohen-Macaulay modules over a Cohen-Macaulay complete local algebra of finite representation type are obtained by iteration of extended degenerations of Auslander-Reiten sequences.

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