Smooth Fano Polytopes With Many Vertices

TL;DR

This paper classifies certain high-vertex smooth Fano polytopes, advancing understanding in algebraic geometry and physics by extending previous classifications of these polytopes.

Contribution

It provides a complete classification of d-dimensional simplicial, terminal, reflexive polytopes with at least 3d-2 vertices, showing they are all smooth Fano polytopes.

Findings

All classified polytopes are smooth Fano polytopes.

Improves previous classification results from 2006 and 2008.

Highlights the role of these polytopes in algebraic geometry and physics.

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.