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

 

Jet schemes of the commuting matrix pairs scheme


Authors: B. A. Sethuraman and Klemen Sivic
Journal: Proc. Amer. Math. Soc. 137 (2009), 3953-3967
MSC (2000): Primary 14M99
Published electronically: July 30, 2009
MathSciNet review: 2538555
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Abstract: We show that for all $ k\ge 1$ there exists an integer $ N(k)$ such that for all $ n\ge N(k)$ the $ k$-th order jet scheme over the commuting $ n\times n$ matrix pairs scheme is reducible.

At the other end of the spectrum, it is known that for all $ k\ge 1$ the $ k$-th order jet scheme over the commuting $ 2\times 2$ matrices is irreducible; we show that the same holds for $ n=3$.


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Additional Information

B. A. Sethuraman
Affiliation: Department of Mathematics, California State University, Northridge, Northridge, California 91330
Email: al.sethuraman@csun.edu

Klemen Sivic
Affiliation: Institute of Mathematics, Physics, and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: klemen.sivic@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10029-1
PII: S 0002-9939(09)10029-1
Received by editor(s): November 4, 2008
Received by editor(s) in revised form: February 19, 2009
Published electronically: July 30, 2009
Additional Notes: The first author was supported by the National Science Foundation grant DMS-0700904.
The second author was supported by the Slovenian Research Agency.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.