On \(\mathcal {GL}_n\)-invariant algebraic cones of matrices with relative codimension equal to 1 (Q2752308)

Let the group \(G\) of invertible \(n\times n\) matrices over a field \(F\) act on the space \(M\) of all \(n\times n\) matrices over \(F\) by conjugation. A map \({\mathbb{N}} \rightarrow {\mathbb{N}}\) which is non-increasing and satisfies a certain convexity condition is called a \textit{rank function}.NEWLINENEWLINENEWLINEThe relative codimension of a subvariety of \(M\) is defined in terms of a given rank function. The author gives a characterization of \(G\)-invariant subcones of \(M\) of relative codimension one in case \(F\) is algebraically closed and of characteristic zero. NEWLINENEWLINENEWLINESee also the following review: \textit{M. Skrzyński}, ibid. 41, 183-193 (2001; Zbl 1020.14014)].