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 language | English |
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Pages (from-to) | 165-182 |
Number of pages | 18 |
Journal | JOURNAL OF ALGEBRAIC COMBINATORICS |
Volume | 42 |
Issue number | 1 |
DOIs | |
Publication status | Published - Aug 2015 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Normal polytope
- Very ample polytope
- Koszul polytope
- Regular unimodular triangulation
- POLYTOPES
- PROPERTY
- ALGEBRAS