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Consider the following cubic hypersurface in $\mathbb{P}^5$: $$ X = \{z_0z_3z_5-z_1^2z_5-z_0z_4^2+2z_1z_2z_4-z_2^2z_3 = 0\}\subset\mathbb{P}^5 $$ The singular locus of $X$ is the Veronese surface $V\...

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Mat{Mat}$Consider the general linear group $$ \GL(n) = \left\lbrace \left(\begin{array}{cc} A & C \\ M & B \end{array}\right) \text{ with } A\...