MathDBVery-ampleness conjecture for integral cyclic polytopes
Very-ampleness conjecture for integral cyclic polytopes
An integral cyclic polytope is a cyclic polytope with integral vertices. A lattice polytope is very ample when its associated semigroup is generated up to saturation in the usual toric-geometric sense, and it is normal when every lattice point in every positive dilate is a sum of lattice points of the polytope. Very-ampleness conjecture. If an integral cyclic polytope is very ample, then it is also normal. The source states this as a further conjecture after discussing normality and very ampleness; its resolution is not specified.
Sources & referencesView supporting material
Primary source
Takayuki Hibi, Akihiro Higashitani, Lukas Katthän and Ryota Okazaki, “Normal cyclic polytopes and cyclic polytopes that are not very ample”, arXiv:1202.6117 (2013).
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