A universal tale of determinants and Gröbner bases
Aldo Conca
Abstract
In 1965 Buchberger defined Gröbner bases and an algorithm to compute them. Despite a slow start, already in the eighties Gröbner bases had become the main device for symbolic computations involving polynomials as well as a theoretical tool for the investigation of ideals and varieties via the so-called Gröbner deformation techniques. Rings and algebraic varieties defined by means of determinants are among the most classical objects in commutative algebra, algebraic geometry and invariant theory. By the end of the the eighties the time was ripe for the computation of Gröbner bases of determinantal ideals. We will tell the tale of how (universal) Gröbner bases of determinantal ideals were identified and the key role played by Bernd Sturmfels and his collaborators in this enterprise.