3 problems

Garcia–Stillman–Sturmfels conjecture. The ideal of $\sigma_2(\operatorname{Seg}(\mathbb{P}V_1\times\cdots\times\mathbb{P}V_n))$ is generated by the $3\times 3$ minors of all flatte…

Let $A_1,ots,A_m$ be vector spaces, and let $Seg(\mathbb P A_1^*\times\cdots\times\mathbb P A_m^*)$ denote their Segre variety, with tangential variety…

Let $\operatorname{Seg}(n_1,\ldots,n_k)$ denote the Segre variety with parameters $(n_1,\ldots,n_k)$, and let $d$-defectivity mean that its $d$-secant variety has smaller than the…