The number of vertices of a Fano polytope
The number of vertices of a Fano polytope
Let X be a Gorenstein, ℚ-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.