4 problems

Let $P\subset\mathbb{R}^d$ be a lattice polytope of dimension $d$ and degree $s$. A Cayley polytope is a lattice polytope expressible as a Cayley sum of lattice polytopes. Cayley c…

For a lattice polytope $P$, define its codegree by … For example, the unimodular simplex satisfies $\operatorname{codeg}(\Delta_n)=n+1$. Batyrev–Nill conjecture. There is a functio…

Lattice Cayley polytope conjecture. If

Let $P$ be an $n$-dimensional smooth ${\mathbb Q}$-normal lattice polytope, and let $s$ denote the order of a generalized Cayley polytope. A bound on the dimension is understood in…