On simplicial toric varieties of codimension 2

TL;DR

This paper characterizes certain codimension 2 toric varieties, identifying those minimally defined by three binomials or set-theoretic complete intersections in specific characteristics, revealing their algebraic and geometric properties.

Contribution

It provides a classification of codimension 2 toric varieties based on their defining equations and set-theoretic properties across different characteristics.

Findings

Identifies classes of toric varieties minimally defined by three binomials.

Determines conditions under which these varieties are set-theoretic complete intersections.

Highlights characteristic-dependent properties of these varieties.

Abstract

We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.