= Projective toric variety of a lattice polytope
{title2=$\mathbb P_\Delta$}
For a <lattice polytope> $\Delta$, form the semigroup of lattice points $(m,l)$ with $l\ge0$ and $m\in l\Delta$, using only $(0,0)$ in degree zero. Its semigroup algebra is graded by $l$, and its <Proj construction> gives $\mathbb P_\Delta$. The chart at a lattice vertex $v$ is $\operatorname{Spec}k[\operatorname{cone}(\Delta-v)\cap M]$; these charts give the <normal fan of a polytope> construction. For a polytope of smaller dimension, use its intrinsic affine lattice after translation.
// Target: geometry-and-topology.bigb
Back to article page
