Finitely many smooth d-polytopes with N lattice points

Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Francisco Santos, Hal Schenck

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)301-329
Number of pages29
JournalIsrael journal of mathematics
Issue number1
Early online date28 Mar 2015
Publication statusPublished - Apr 2015


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