Non-very ample configurations arising from contingency tables

TL;DR

This paper investigates the conditions under which certain algebraic structures called semigroup rings, especially those related to contingency tables, are very ample, providing new theoretical insights and classifications.

Contribution

It establishes a criterion linking fundamental binomials in toric ideals to the non-very ampleness of the associated semigroup rings and discusses very ampleness in Lawrence type rings.

Findings

A toric ideal with a fundamental binomial without squarefree monomials implies non-very ampleness.

Analysis of very ample semigroup rings of Lawrence type.

Application to the study of configurations from contingency tables.

Abstract

In this paper, it is proved that, if a toric ideal possesses a fundamental binomial none of whose monomials is squarefree, then the corresponding semigroup ring is not very ample. Moreover, very ample semigroup rings of Lawrence type are discussed. As an application, we study very ampleness of configurations arising from contingency tables.