5 problems

Let $\mathrm{Cat}(2,3)$ be the catalecticant variety, let $\mathbb{P}\\,\mathrm{Cat}(2,3)^{-1}$ denote its reciprocal variety, and let a cubic Pfaffian mean the Pfaffian of a…

Let $C_1$ denote the rank-one locus of the relevant catalecticant variety, let $A$ be a point on $C_1$, and let $\phi(A)$ be its image under the map $\phi$. Seven-Pfaffian conjectu…

Let $m\geq 1$ and let an $r$-leap $m\times m$ catalecticant be the corresponding structured matrix of linear forms, with $1\leq r\leq m$. The linear syzygy rank of a gradient ideal…

Let $K$ be a field, let $n,d,ke\mathbb{Z}$ with $k,n\geq 2$ and $d\geq 2k-2$, and let $Cat(t,d-t;n)$ denote the $t$-th generic catalecticant. Write $I_k(Cat(t,d-t;n))$ for the idea…

Let $v_d(\mathbb P V)\vartriangleleft\mathbb P S^dV$ be the Veronese variety, and let $\sigma_2(v_{d+e}(\mathbb P^n))$ be its second secant variety. The determinantal ideal from th…