Finitely many smooth d-polytopes with n lattice points
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- Bogart, T., Haase, C., Hering, M. et al. Isr. J. Math. (2015) 207: 301. doi:10.1007/s11856-015-1175-7
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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.