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A classification of smooth convex 3-polytopes with at most 16 lattice points

By Anders Lundman


We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining 4 are obtained as inverse stellar subdivisions of such polytopes. We derive a classification, up to isomorphism, of all smooth embeddings of toric threefolds in $\mathbb{P}^N$ where $N\le 15$. Again we have in total 103 such embeddings. Of these, 99 are projective bundles embedded in $\mathbb{P}^N$ and the remaining 4 are blow-ups of such toric threefolds.Comment: 25 pages, 130 figures; Journal of Algebraic Combinatorics Online First, 201

Topics: Mathematics - Combinatorics, Mathematics - Algebraic Geometry
Publisher: 'Springer Science and Business Media LLC'
Year: 2012
DOI identifier: 10.1007/s10801-012-0363-3
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