Non-normal very ample polytopes - constructions and examples

TL;DR

This paper introduces a method to construct non-normal very ample polytopes using segmental fibrations of unimodular graph polytopes, and computes their key invariants, addressing several open questions in the field.

Contribution

It provides a novel construction technique for non-normal very ample polytopes and explicitly computes their invariants, advancing understanding in polytope theory.

Findings

Constructed new classes of non-normal very ample polytopes.

Explicitly computed Hilbert functions and Ehrhart polynomials for these polytopes.

Answered several open questions related to polytope invariants.

Abstract

We present a method of constructing non-normal very ample polytopes as a segmental fibration of unimodular graph polytopes. In many cases we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, gap vector. In particular, we answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani and Maclagan.