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- W2949506177 abstract "Let $N(d,n)$ be the variety of all $d$-tuples of commuting nilpotent $ntimes n$ matrices. It is well-known that $N(d,n)$ is irreducible if $d=2$, if $nle 3$ or if $d=3$ and $n=4$. On the other hand $N(3,n)$ is known to be reducible for $nge 13$. We study in this paper the reducibility of $N(d,n)$ for various values of $d$ and $n$. In particular, we prove that $N(d,n)$ is reducible for all $d,nge 4$. In the case $d=3$, we show that it is irreducible for $nle 6$." @default.
- W2949506177 created "2019-06-27" @default.
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- W2949506177 date "2013-08-20" @default.
- W2949506177 modified "2023-09-27" @default.
- W2949506177 title "On varieties of commuting nilpotent matrices" @default.
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