Gröbner Bases of Determinantal Ideals

Abstract

Chapter 4 presents the computation of Gröbner bases, based on standard bitableaux and the Robinson-Schensted-Knuth correspondence to which it gives a short introduction. It exploits the information on the initial ideal for structural results with a homological flavor, as well as in the computation of enumerative data such as multiplicities and Hilbert series. We give also a more recent approach to Gröbner bases of determinantal ideals via secant varieties. © 2022, Springer Nature Switzerland AG.