3 problems

Let $A_1,\dots,A_{m+1}$ be linear operators on ${\mathbb R}^m$, and let ${\mathcal X}$ be their degeneracy locus in ${\mathbb P}^{m-1}({\mathbb R})$. The locus has expected dimensi…

Let $A_1,\dots,A_5$ be real matrices whose degeneracy locus ${\mathcal X}:={\mathcal X}(A_1,\dots,A_5)$ is formed from the associated ten lines in ${\mathbb P}^3$. Desargues config…

Constant-rank matrix dimension conjecture. Then