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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
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References:
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