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Very ample and Koszul segmental fibrations

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2015

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Beck, Matthias
Delgado, Jessica
Gubeladze, Joseph

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https://doi.org/10.1007/s10801-014-0577-7
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Physik: Publikationen
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Journal of Algebraic Combinatorics. Springer. 2015, 42(1), pp. 165-182. ISSN 0925-9899. eISSN 1572-9192. Available under: doi: 10.1007/s10801-014-0577-7

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Normal polytope, Very ample polytope, Koszul polytope, Regular unimodular triangulation

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ISO 690BECK, Matthias, Jessica DELGADO, Joseph GUBELADZE, Mateusz MICHALEK, 2015. Very ample and Koszul segmental fibrations. In: Journal of Algebraic Combinatorics. Springer. 2015, 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},
  author={Beck, Matthias and Delgado, Jessica and Gubeladze, Joseph and Michalek, Mateusz}
}
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