### 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 | |

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

## Fingerprint Dive into the research topics of 'Examples of degenerations of Cohen-Macaulay modules'. Together they form a unique fingerprint.

## Cite this

Hiramatsu, N., & Yoshino, Y. (2013). Examples of degenerations of Cohen-Macaulay modules.

*Proceedings of the American Mathematical Society*,*141*(7), 2275-2288. https://doi.org/10.1090/S0002-9939-2013-11523-6