The number of vertices of a Fano polytope
Algebraic Geometry
2007-05-23 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.math/0411073,
title = {The number of vertices of a Fano polytope},
author = {C. Casagrande},
journal= {arXiv preprint arXiv:math/0411073},
year = {2007}
}
Comments
Final version, to appear in Annales de l'Institut Fourier