Israel Journal of Mathematics

, Volume 207, Issue 1, pp 301–329 | Cite as

Finitely many smooth d-polytopes with n lattice points

  • Tristram Bogart
  • Christian Haase
  • Milena Hering
  • Benjamin Lorenz
  • Benjamin Nill
  • Andreas Paffenholz
  • Günter Rote
  • Francisco Santos
  • Hal Schenck
Article

Abstract

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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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  • Tristram Bogart
    • 1
  • Christian Haase
    • 2
  • Milena Hering
    • 3
  • Benjamin Lorenz
    • 4
  • Benjamin Nill
    • 5
  • Andreas Paffenholz
    • 6
  • Günter Rote
    • 7
  • Francisco Santos
    • 8
  • Hal Schenck
    • 9
  1. 1.Universidad de los AndesBogotáColombia
  2. 2.Goethe-UniversitätFrankfurt am MainGermany
  3. 3.School of MathematicsThe University of EdinburghEdinburghRussia
  4. 4.Institut für Mathematik, Sekretariat MATechnische Universität BerlinBerlinGermany
  5. 5.Matematiska institutionenStockholms UniversitetStockholmSweden
  6. 6.Technische Universität DarmstadtDarmstadtGermany
  7. 7.Institut für InformatikFreie Universität BerlinBerlinGermany
  8. 8.Dept. Matematicas, Estad. y Comp.Universidad de CantabriaSantanderSpain
  9. 9.Mathematics DepartmentUniversity of IllinoisUrbanaUSA

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