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The depth of a reflexive polytope. (English) Zbl 1418.13015
Summary: Given arbitrary integers $$d$$ and $$r$$ with $$d \ge 4$$ and $$1 \le r \le d + 1$$, a reflexive polytope $${\mathscr{P}}\subset{\mathbb R}^d$$ of dimension $$d$$ with $$\text{depth}\,K[{\mathscr{P}}] = r$$ for which its dual polytope $${\mathscr{P}}^\vee$$ is normal will be constructed, where $$K[{\mathscr{P}}]$$ is the toric ring of $${\mathscr{P}}$$.
##### MSC:
 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
##### Software:
Macaulay2; Normaliz
Full Text:
##### References:
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