Vaibhav Pandey

The variety of nilpotent matrices is $F$-regular

We give an elementary proof that the coordinate ring of the variety of nilpotent matrices is $F$-regular; over an infinite field $K$, this ring also arises as the nullcone for the conjugation action of the general linear group $\textrm{GL}_n(K)$ on the polynomial ring $K[X]$, where $X$ is an $n\times n$ matrix of indet...