Equivalence classes for smooth Fano polytopes

2015/03/22 by Higashitani, Akihiro
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 14M25 #Secondary 52B20

paper · doi:10.48550/arxiv.1503.06434

Abstract

Let F(n) be the set of smooth Fano n-polytopes up to unimocular equivalence. In this paper, we consider the F-equivalence or I-equivalence classes for F(n) and introduce F-isolated or I-isolated smooth Fano n-polytopes. First, we describe all of F-equivalence classes and I-equivalence classes for F(5). We also give a complete characterization of F-equivalence classes (I-equivalence classes) for smooth Fano n-polytopes with n+3 vertices and construct a family of I-isolated smooth Fano polytopes.

Related

• An algorithm for the classification of smooth Fano polytopes
• Smooth Fano polytopes arising from finite partially ordered sets
• Unimodular Smooth Fano Polytopes and their Relation with Ewald Conditions
• A bound for the splitting of smooth Fano polytopes with many vertices
• Gorenstein Fano polytopes arising from order polytopes and chain polytopes