Binomial canonical decompositions of binomial ideals

TL;DR

This paper proves that binomial ideals in polynomial rings over algebraically closed fields of characteristic zero have a unique, canonical primary decomposition into binomial ideals, derived from a canonical cellular decomposition.

Contribution

It establishes the existence and canonicity of primary decompositions for binomial ideals, linking them to cellular decompositions independent of the field.

Findings

Existence of canonical primary decomposition for binomial ideals

Decomposition derived from a canonical cellular decomposition

Independence of the decomposition from the base field

Abstract

In this paper, we prove that every binomial ideal in a polynomial ring over an algebraically closed field of characteristic zero admits a canonical primary decomposition into binomial ideals. Moreover, we prove that this special decomposition is obtained from a cellular decomposition which is also defined in a canonical way and does not depend on the field.