Smooth Fano Polytopes With Many Vertices
arXiv:1209.3186 · doi:10.1007/s00454-014-9607-4
Abstract
We classify the d-dimensional simplicial, terminal, and reflexive polytopes with at least 3d-2 vertices. In particular, it turns out that these are all smooth Fano polytopes. This improves on previous results of Casagrande in 2006 and Oebro in 2008. Smooth Fano polytopes play a role in algebraic geometry and mathematical physics.
34 pages, to appear in Discrete & Computational Geometry