Combinatorics of binomial primary decomposition

TL;DR

This paper provides a combinatorial method to explicitly describe the primary decomposition of binomial ideals in characteristic zero, linking algebraic structures to hypergeometric differential equations.

Contribution

It introduces a characteristic-free combinatorial framework for primary components of binomial ideals associated with faces of affine semigroups.

Findings

Explicit lattice point realization for primary components

Characteristic-free combinatorial description

Connection to hypergeometric differential equations

Abstract

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hypergeometric differential equations in several variables.