## Very ample and Koszul segmental fibrations

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2015
Beck, Matthias
Journal article
Published
##### Published in
Journal of Algebraic Combinatorics ; 42 (2015), 1. - pp. 165-182. - Springer. - ISSN 0925-9899. - eISSN 1572-9192
##### 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.
510 Mathematics
##### Keywords
Normal polytope, Very ample polytope, Koszul polytope, Regular unimodular triangulation
##### Cite This
ISO 690BECK, Matthias, Jessica DELGADO, Joseph GUBELADZE, Mateusz MICHALEK, 2015. Very ample and Koszul segmental fibrations. In: Journal of Algebraic Combinatorics. Springer. 42(1), pp. 165-182. ISSN 0925-9899. eISSN 1572-9192. Available under: doi: 10.1007/s10801-014-0577-7
BibTex
@article{Beck2015ample-52338,
year={2015},
doi={10.1007/s10801-014-0577-7},
title={Very ample and Koszul segmental fibrations},
number={1},
volume={42},
issn={0925-9899},
journal={Journal of Algebraic Combinatorics},
pages={165--182},
}

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