Complete intersections in binomial and lattice ideals

TL;DR

This paper provides criteria for when graded lattice ideals of dimension 1 are complete intersections, showing that in positive characteristic all such ideals are binomial set theoretic complete intersections, and in characteristic zero, these are exactly the binomial set theoretic complete intersections that are complete.

Contribution

It establishes a complete intersection criterion for graded lattice ideals of dimension 1 and characterizes binomial set theoretic complete intersections in different characteristics.

Findings

In positive characteristic, all ideals in the family are binomial set theoretic complete intersections.

In characteristic zero, binomial set theoretic complete intersections are exactly the complete intersections.

Provides algebraic and geometric criteria for complete intersections in lattice ideals.

Abstract

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set theoretic complete intersection is a complete intersection.