Finitely many smooth d-polytopes with n lattice points

@article{Bogart2015FinitelyMS,
  title={Finitely many smooth d-polytopes with n lattice points},
  author={Tristram Bogart and Christian Haase and Milena Hering and Benjamin Lorenz and Benjamin Nill and Andreas Paffenholz and G{\"u}nter Rote and Francisco Santos and Hal Schenck},
  journal={Israel Journal of Mathematics},
  year={2015},
  volume={207},
  pages={301-329}
}
We prove that for fixed n there are only finitely many embeddings of ℚ-factorial toric varieties X into ℙn that are induced by a complete linear system. The proof is based on a combinatorial result that implies that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with ≤ 12 lattice points. 
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