2014•Unpublished venueRequires access

SMOOTH FANO POLYTOPES WITH MANY VERTICES

Benjamin Assarf, Michael Joswig, Andreas Paffenholz

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.

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Key concepts: Polytope, Fano plane, Combinatorics, Algebraic number, Mathematics, Pure mathematics, Mathematical analysis