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Unimodular triangulations of sufficiently large dilations
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abstract
An integral polytope is a polytope whose vertices have integer coordinates. A unimodular triangulation of an integral polytope in $\mathbb{R}^d$ is a triangulation in which all simplices are integral with volume $1/d!$. A classic result of Knudsen, Mumford, and Waterman states that for every integral polytope $P$, there exists a positive integer $c$ such that $cP$ has a unimodular triangulation. We strengthen this result by showing that for every integral polytope $P$, there exists $c$ such that for every positive integer $c' \ge c$, $c'P$ admits a unimodular triangulation. This answers a longstanding question in the area.
Forward citations
Cited by 2 Pith papers
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Mirrors to toric degenerations via intrinsic mirror symmetry
For special toric degenerations of K3 surfaces, the intrinsic mirror and the universal toric degeneration mirror coincide after restricting to the minimal relative Gross-Siebert locus and basechanging by the polarization.
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On the magic positivity of Ehrhart polynomials of dilated polytopes
For every polynomial with positive coefficients, all sufficiently large dilations are magic positive, and the paper introduces the m-index to measure this threshold for Ehrhart polynomials of polytopes.
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