Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties)
We prove that the sheets of \(gl_ n\) are rational varieties. Furthermore, generalizing the well-known concept of the companion-matrix of a polynomial, we construct affine subspaces of \(gl_ n\) which are transversal cross-sections. Our construction is somewhat easier to understand than Petersons cross-sections. Moreover, all our results and proofs are true also in positive characteristic.
scientific article; zbMATH DE number 4043995