2 problems

Bøgvad's conjecture. The toric ideal $I_P$ is quadratic.

Let $P\subset\mathbb{R}^d$ be a lattice polytope, and let ${\mathcal A}_P=\{(\alpha,1)\in\mathbb{Z}^{d+1}:\alpha\in P\cap\mathbb{Z}^d\}$. The toric ideal of $P$ is the kernel of th…