4 problems

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $M=\operatorname{M}(L)$, and let $F$ be a flat of $M$. Write…

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $L^{-1}$ be its reciprocal linear space, and let…

Degree conjecture. If the matroid $M(L)$ is connected, then $\nabla(L^{-1})$ is a hypersurface of degree

Dual-defectivity conjecture. The reciprocal linear space $L^{-1}$ is dual defective, meaning