Geodesic
Very ample and Koszul segmental fibrations
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 165-182.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 52B20, 14M25, 13P10
Keywords: normal polytope, very ample polytope, Koszul polytope, regular unimodular triangulation 
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     title = {Very ample and {Koszul} segmental fibrations},
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Beck, Matthias; Delgado, Jessica; Gubeladze, Joseph; Michałek, Mateusz. Very ample and Koszul segmental fibrations. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 165-182. http://geodesic.mathdoc.fr/item/JAC_2015__42_1_a5/