An algorithm for the classification of smooth Fano polytopes
Mikkel {\O}bro
TL;DR
This paper introduces an algorithm capable of classifying smooth Fano polytopes in any dimension, successfully applied to dimensions up to 7, revealing thousands of isomorphism classes.
Contribution
The paper presents a novel algorithm for classifying smooth Fano polytopes across all dimensions, with comprehensive results for dimensions 6 and 7.
Findings
7622 classes of smooth Fano 6-polytopes identified
72256 classes of smooth Fano 7-polytopes identified
Algorithm effectively classifies polytopes up to dimension 7
Abstract
We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Geometric and Algebraic Topology