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29 March 2024
 
  » arxiv » 1010.3887

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Few smooth d-polytopes with N lattice points
Tristram Bogart ; Christian Haase ; Milena Hering ; Benjamin Lorenz ; Benjamin Nill ; Andreas Paffenholz ; Francisco Santos ; Hal Schenck ;
Date 19 Oct 2010
AbstractWe prove that, for fixed N there exist only finitely many embeddings of Q-factorial toric varieties X into P^N that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and N, there are only finitely many smooth d-polytopes with N lattice points. The argument is turned into an algorithm to classify smooth 3-polytopes with le 12 lattice points.
Source arXiv, 1010.3887
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