11 problems

Conjecture on the components of $\mathcal{SC}_r$. For all $r\in[N+1]$:

Let $P$ be an integral polytope. A polytope is called a defect polytope when its associated projective toric variety has degenerate dual variety, equivalently when the invariant…

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

Let $N$ be the matrix-size parameter, let $[N+1]=\{1,\ldots,N+1\}$, and let $S=S^2\mathbb{C}^{N+1}$ be the subspace of symmetric $(N+1)\times(N+1)$ matrices. For $r\in[N+1]$, defin…

Landman's duality defect conjecture. If

Abuaf's dimension conjecture. One has

Let a weighted projective space be a projective toric variety, and call it defective when its dual variety is not a hypersurface. A cone over a weighted projective space is a weigh…

The dual-defective-to-LQEL conjecture. $X$ is a local quadratic entry locus manifold (LQELM).

Let $X\subset\mathbb{P}^n$ be a smooth, irreducible, non-degenerate projective variety. For each $r\in\{0,\ldots,n\}$, define … where $p(q^{-1}(H^{\bot}))$ is the contact locus of…

Let $X \subset \mathbb{P}_{\mathbb{C}}^n$ be a non-degenerate, irreducible projective variety, and let $X^* \subset \mathbb{P}_{\mathbb{C}}^N$ be its projective dual. For…