Beck, Matthias; Delgado, Jessica; Gubeladze, Joseph; Michałek, Mateusz

Very ample and Koszul segmental fibrations

J. Algebr. Comb. 42(1), 165-182 (2015)
DOI: 10.1007/s10801-014-0577-7

Summary

In the hierarchy of structural sophistication for lattice polytopes, normal polytopes mark a point of origin; very ample and Koszul polytopes occupy bottom and top spots in this hierarchy, respectively. In this paper we explore a simple construction for lattice polytopes with a twofold aim. On the one hand, we derive an explicit series of very ample 3-dimensional polytopes with arbitrarily large deviation from the normality property, measured via the highest discrepancy degree between the corresponding Hilbert functions and Hilbert polynomials. On the other hand, we describe a large class of Koszul polytopes of arbitrary dimensions, containing many smooth polytopes and extending the previously known class of Nakajima polytopes.

Mathematics Subject Classification

52B20, 14M25, 13P10

Keywords/Phrases

normal polytope, very ample polytope, Koszul polytope, regular unimodular triangulation

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