7 problems

Oeding's conjecture. All secant varieties of Segre products of projective spaces are arithmetically Cohen–Macaulay; equivalently, $\widehat{\sigma}_r$ is Cohen–Macaulay for every…

Projective-equivalence conjecture. The subsets $S\in X$ of cardinality $6$ such that $\pi_i(S)$ and $\pi_j(S)$ are projectively equivalent, for some fixed $i\neq j$, fill a dense o…

Segre–split secant conjecture. If $m\geq 1$, then $\sigma_s(\operatorname{Seg}(\mathbb P^m\times\operatorname{Split}_d(\mathbb P^n))$ is nondefective for all cases except those out…

Safety-bound conjecture. The following statements hold:

Let $X$ be a Segre variety, and let $I(\tau(X))$ denote the homogeneous ideal of its tangential variety. The relevant Schur-module factors are expressed using exterior powers…

Let $V$ be a vector space and let $p\in\mathbb P S^dV\vartriangleleft\mathbb P(V^{\otimes d})$. Let $R_{v_d(\mathbb P V)}(p)$ be the symmetric rank of $p$, and let…

Let $A_j=A_j'\oplus A_j”$ be decompositions of vector spaces, and set … Let $X=\operatorname{Seg}(\mathbb P A_1\times\cdots\times\mathbb P A_k)$, and let $R_X$ denote the $X$-rank.…