Determinantal variety

Summary

A determinantal variety is the set of matrices of a fixed size whose rank is at most a given number. It is cut out by the vanishing of all minors of one size larger, which generate a determinantal ideal. These varieties are irreducible, normal and Cohen–Macaulay, and they are basic examples of singular varieties. Many varieties in geometry, such as secant varieties and rational normal curves, are described by determinantal equations.