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


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


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