Smooth Fano Polytopes With Many Vertices
Algebraic Geometry
2015-07-31 v3 Combinatorics
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.
Cite
@article{arxiv.1209.3186,
title = {Smooth Fano Polytopes With Many Vertices},
author = {Benjamin Assarf and Michael Joswig and Andreas Paffenholz},
journal= {arXiv preprint arXiv:1209.3186},
year = {2015}
}
Comments
34 pages, to appear in Discrete & Computational Geometry