On toric varieties of high arithmetical rank

TL;DR

This paper introduces a class of high-dimensional toric varieties characterized by their minimal defining equations, which are binomials, highlighting their algebraic complexity.

Contribution

It identifies a specific class of toric varieties in affine space that require at least N-2 binomial equations for their minimal definition, advancing understanding of their algebraic structure.

Findings

Toric varieties with high arithmetical rank are characterized.

Minimal defining equations for these varieties are binomials.

The class of varieties described requires at least N-2 binomial equations.

Abstract

We describe a class of toric varieties in the $N$-dimensional affine space which are minimally defined by no less than $N-2$ binomial equations.