Decompositions of Cellular Binomial Ideals

TL;DR

This paper develops methods to decompose cellular binomial ideals into their primary components, providing explicit decompositions over algebraically closed fields and confirming a conjecture on unmixed decompositions.

Contribution

It proves a conjecture by Eisenbud and Sturmfels and offers explicit primary decompositions for cellular binomial ideals without restrictions on the base field.

Findings

Computed the hull of cellular binomial ideals.

Proved a conjecture on unmixed decompositions.

Provided explicit primary decompositions over algebraically closed fields.

Abstract

Without any restrictions on the base field, we compute the hull and prove a conjecture of Eisenbud and Sturmfels giving an unmixed decomposition of a cellular binomial ideal. Over an algebraically closed field, we further obtain an explicit (but not necessarily minimal) primary decomposition of such an ideal.