Few smooth d-polytopes with n lattice points
Algebraic Geometry
2015-09-22 v2 Combinatorics
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1010.3887,
title = {Few smooth d-polytopes with n lattice points},
author = {Tristram Bogart and Christian Haase and Milena Hering and Benjamin Lorenz and Benjamin Nill and Andreas Paffenholz and Günter Rote and Francisco Santos and Hal Schenck},
journal= {arXiv preprint arXiv:1010.3887},
year = {2015}
}
Comments
20+2 pages; major revision: new author, new structure, new results