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

doi:10.1007/s11856-015-1175-7

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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. The argument is turned into an algorithm to classify smooth 3-polytopes with \le 12 lattice points.

Original language	English
Pages (from-to)	301-329
Number of pages	29
Journal	Israel journal of mathematics
Volume	207
Issue number	1
Early online date	28 Mar 2015
DOIs	https://doi.org/10.1007/s11856-015-1175-7
Publication status	Published - Apr 2015

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finitely many smooth d-polytopes with n lattice pointsSubmitted manuscript, 2.96 MB

Milena Hering
- School of Mathematics - Reader
Person: Academic: Research Active

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title = "Finitely many 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\textasciicircum{}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 \textbackslash{}le 12 lattice points.",

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AU - Haase, Christian

AU - Hering, Milena

AU - Lorenz, Benjamin

AU - Nill, Benjamin

AU - Paffenholz, Andreas

AU - Santos, Francisco

AU - Schenck, Hal

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N2 - 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.

AB - 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.

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DO - 10.1007/s11856-015-1175-7

M3 - Article

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VL - 207

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EP - 329

JO - Israel journal of mathematics

JF - Israel journal of mathematics

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Finitely many smooth d-polytopes with N lattice points

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Milena Hering

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