The number of vertices of a Fano polytope
arXiv:math/0411073
Abstract
Let X be a complex, 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.
Final version, to appear in Annales de l'Institut Fourier