3 problems

Sebő's conjecture. The ICP holds for every $n$-dimensional cone $C$.

Let $C(\bm{A})$ be a cone, let $-\bm{a}\in C(\bm{A})^*\cap\mathbb{Z}^n$, and let $\bm{h}\in C(\bm{A})$ be a Hilbert basis element with respect to $\mathbb{Z}^n$. Weak Hilbert basis…

Henk–Weismantel conjecture. Every minimal solution lies in this convex hull: