Few smooth d-polytopes with n lattice points

Abstract

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. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.

20+2 pages; major revision: new author, new structure, new results

References in corpus (3)

• Canonical toric Fano threefolds
• On the combinatorial classification of toric log del Pezzo surfaces
• A classification of smooth convex 3-polytopes with at most 16 lattice points

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