Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties) (Q1100532)
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scientific article; zbMATH DE number 4043995
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties) |
scientific article; zbMATH DE number 4043995 |
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Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties) (English)
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1989
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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.
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sheets of matrices
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transversal cross-sections
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positive characteristic
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elementary divisor
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