2 problems

Let $X$ be a closed irreducible subvariety of the hyperplane $H=\{(p_1,\ldots,p_n)\in({\mathbb{C}}^*)^n:p_1+\cdots+p_n=1\}$, and let $d=\dim X$. The Huh–Sturmfels conjecture. One h…

Let $X$ be an irreducible algebraic subvariety of $({\mathbb C}^*)^n$ contained in … and let $\bar X$ be its closure in $({\mathbb C}^*)^{n-1}\times{\mathbb C}$. Suppose that…