September 29, 2025Open Access

An Early History of Toric Ideals

Key Points

Toric ideals emerged in commutative algebra around 1990, highlighting new results in the field.
Bernd Sturmfels has been a pivotal figure in promoting toric ideals and their applications through various collaborations.
The development of Gröbner bases marked significant advancements in understanding toric ideals.
This narrative reflects on the first decade of toric ideals and their impactful evolution.

Abstract

Toric ideals are everywhere. They have been in the commutative algebra lexicon since about 1990 when Bernd Sturmfels used the term. The early days of toric ideals and their Gr\"obner bases were full of new results and promising developments in their applications. Bernd has been consistently their biggest promoter through his own work and that of his collaborators and students. This article is a personal and subjective recalling of the first decade of toric ideals when Bernd played a central role.

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Cite This Study

Serkan Hoşten (Fri,) studied this question.

synapsesocial.com/papers/68da58d8c1728099cfd110b2 https://doi.org/https://doi.org/10.48550/arxiv.2505.18443

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