An Early History of Toric Ideals

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 Gröbner 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.

To appear in AMS PSPUM Volume "Combinatorial, Computational, and Applied Algebraic Geometry: A Tribute to Bernd Sturmfels"