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arXiv · 1307.7422

Very ample and Koszul segmental fibrations

Matthias Beck·Jessica Delgado·Joseph Gubeladze·Mateusz Michałek
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Abstract

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.

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Matthias Beck, Jessica Delgado, Joseph Gubeladze, Mateusz Michałek. 2014-12-05. Very ample and Koszul segmental fibrations. https://arxiv.org/abs/1307.7422

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