Examples of degenerations of Cohen-Macaulay modules

Naoya Hiramatsu; Yuji Yoshino

doi:10.1090/S0002-9939-2013-11523-6

Examples of degenerations of Cohen-Macaulay modules

Naoya Hiramatsu, Yuji Yoshino

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2275-2288
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-2013-11523-6
Publication status	Published - Apr 24 2013

Keywords

Auslander-Reiten Sequence
Cohen-Macaulay module
Degeneration
Finite representation type

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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N2 - 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 (An) 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.

AB - 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 (An) 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.

KW - Auslander-Reiten Sequence

KW - Cohen-Macaulay module

KW - Degeneration

KW - Finite representation type

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