5 problems

Let $SV_{\mathbf{d},\mathbf{n}}$ be a Segre-Veronese variety, let $\sigma_{\mathbf{r}}(SV_{\mathbf{d},\mathbf{n}})$ denote its secant variety, and let a Hadamard product mean the c…

Let $k>1$, let $\boldsymbol{E}=S^{\delta_{1}}(E_{1})\otimes \cdots \otimes S^{\delta_{k}}(E_{k})$, where at least one $\delta_i>1$, and let $\Xi_r(\boldsymbol{E})$ be the $r$-secan…

Non-defectivity conjecture for degrees at least $(3,3)$. There are no defective two-factor Segre-Veronese varieties $X_{\mathbf{n},\mathbf{a}}$ for any $\mathbf{n}\in\mathbb{N}^2$.

Defective Segre-Veronese conjecture. The variety $X_{\mathbf{n},\mathbf{a}}$ is defective if and only if $(\mathbf{n},\mathbf{a})$ falls into one of the following cases:

The defective secant-variety conjecture. The variety $\sigma_s(X_{m,n})$ is defective if and only if $(m,n,s)$ falls into one of the following cases: