3 problems

Let $n=\sum_{j=1}^k n_j$ and consider a $(k+1)$-tensor space $V$ of format $(n_1+1,\dots,n_k+1,n+2)$, with $T\in V$ a general tensor. Higher-factor defective-span conjecture. If…

Let $T$ be a general tensor of format $(a+1,b+1,n+2)$, where $n=a+b$ and $a,b\geq2$. Three-factor defective-span conjecture. … except in the cases $(3,3,6)$, $(3,4,7)$, and…

Let $X\subset \mathbb{P}^r$ be a defective reduced and irreducible projective variety, let $k\geq 0$, and let $\nu_k(X)$ and $\delta_k(X)$ denote respectively the dimension of its…