Sums of toric ideals

TL;DR

This paper investigates conditions under which the sum of multiple toric ideals remains a toric ideal, providing necessary criteria for such algebraic structures.

Contribution

It introduces necessary conditions for the sum of several toric ideals to be toric, expanding understanding of their algebraic behavior.

Findings

Identifies conditions for sums of two toric ideals to be toric

Provides criteria for sums of multiple toric ideals

Advances theoretical understanding of toric ideal combinations

Abstract

Given two toric ideals $I_1,I_2\subset\si$, it is not always true that $I_1+I_2$ is a toric ideal. Given $I_1,...,I_k\subset\si$ a familly of toric ideals we give necessary conditions in order to have that $I_1+...+I_k$ is a toric ideal.