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Classification of smooth Fano polytopes

by Mikkel Øbro
PhD Dissertations January 2008

A simplicial lattice polytope containing the origin in the interior is called a smooth Fano polytope, if the vertices of every facet is a basis of the lattice. The study of smooth Fano polytopes is motivated by their connection to toric varieties.

The thesis concerns the classification of smooth Fano polytopes up to isomorphism.

A smooth Fano d-polytope can have at most 3d vertices. In case of 3d vertices an explicit classification is known. The thesis contains the classification in case of 3d1 vertices.

Classifications of smooth Fano d-polytopes for fixed d exist only for d5. In the thesis an algorithm for the classification of smooth Fano d-polytopes for any given d is presented. The algorithm has been implemented and used to obtain the complete classification for d8.

Format available: PDF (1 MB)
Thesis advisor: Johan P. Hansen