Chandrasekhar Hall
The Singular tuples of matrices is not a null cone
K V Subrahmanyam
CMI
We say an m tuple of $n \times n$ matrices $(X_1, X_2,\ldots,X_m)$ is a singular tuple if the (complex) linear span of $X_1,X_2,\ldots,X_m$
contains only matrices with determinant zero. A natural question is if there some reductive group $G$ acting linearly on $C^{mn^2}$ such that
the null cone for the action is precisely singular tuples of matrices. Recently Vishwambara Makam and Avi Wigderson showed that
this is not possible, if either $m \geq 3$ or $n \geq 3$. I will give a sketch of their proof.
Done