Very ample and Koszul segmental fibrations

Matthias Beck*, Jessica Delgado, Joseph Gubeladze, Mateusz Michalek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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.

Original languageEnglish
Pages (from-to)165-182
Number of pages18
JournalJOURNAL OF ALGEBRAIC COMBINATORICS
Volume42
Issue number1
DOIs
Publication statusPublished - Aug 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Normal polytope
  • Very ample polytope
  • Koszul polytope
  • Regular unimodular triangulation
  • POLYTOPES
  • PROPERTY
  • ALGEBRAS

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