Finitely many smooth d-polytopes with n lattice points View Full Text


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Article Info

DATE

2015-03-28

AUTHORS

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

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. More... »

PAGES

301-329

References to SciGraph publications

  • 2004-04. The Minimum Area of Convex Lattice n-Gons in COMBINATORICA
  • 2012-03-30. A classification of smooth convex 3-polytopes with at most 16 lattice points in JOURNAL OF ALGEBRAIC COMBINATORICS
  • 2000. polymake: a Framework for Analyzing Convex Polytopes in POLYTOPES — COMBINATORICS AND COMPUTATION
  • 1996. Combinatorial Convexity and Algebraic Geometry in NONE
  • 2010. Generating Smooth Lattice Polytopes in MATHEMATICAL SOFTWARE – ICMS 2010
  • 1995. Lectures on Polytopes, Updated Seventh Printing of the First Edition in NONE
  • 2002-05. On generators of ideals defining projective toric varieties in MANUSCRIPTA MATHEMATICA
  • 1999-03. On the classification of toric Fano 4-folds in JOURNAL OF MATHEMATICAL SCIENCES
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    http://scigraph.springernature.com/pub.10.1007/s11856-015-1175-7

    DOI

    http://dx.doi.org/10.1007/s11856-015-1175-7

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