Jet schemes of the commuting matrix pairs scheme

Sethuraman, B.; Šivic, Klemen

doi:10.1090/S0002-9939-09-10029-1

Jet schemes of the commuting matrix pairs scheme
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by B. A. Sethuraman and Klemen Šivic

Proc. Amer. Math. Soc. 137 (2009), 3953-3967

DOI: https://doi.org/10.1090/S0002-9939-09-10029-1

Published electronically: July 30, 2009

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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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