Few smooth d-polytopes with N lattice points

Details Few smooth d-polytopes with N lattice points Few smooth d-polytopes with N lattice points

2010-10-19

arxiv.org/abs/1010.3887v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We 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.

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