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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Examples of degenerations of Cohen-Macaulay modules


Authors: Naoya Hiramatsu and Yuji Yoshino
Journal: Proc. Amer. Math. Soc. 141 (2013), 2275-2288
MSC (2010): Primary 13C14; Secondary 13D10, 16G50, 16G60, 16G70
Published electronically: March 22, 2013
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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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Additional Information

Naoya Hiramatsu
Affiliation: Department of General Education, Kure National College of Technology, 2-2-11, Agaminami, Kure Hiroshima, 737-8506 Japan
Email: hiramatsu@kure-nct.ac.jp

Yuji Yoshino
Affiliation: Department of Mathematics, Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
Email: yoshino@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11523-6
PII: S 0002-9939(2013)11523-6
Keywords: Degeneration, Cohen-Macaulay module, finite representation type, Auslander-Reiten sequence
Received by editor(s): December 24, 2010
Received by editor(s) in revised form: September 2, 2011, and October 20, 2011
Published electronically: March 22, 2013
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society