Configurations of linear subspaces and rational invariants
Abstract
We construct a birational equivalence between certain quotients of s-tuples of equidimensional linear subspaces of $C^n$ and some quotients of products of square matrices modulo diagonal conjugations. In particular, we prove the rationality of the quotient space of s-tuples of linear 2-planes in $C^n$ modulo the diagonal $\gl_n(C)$-action . Furthermore, we compute generators of the field of the rational invariants explicitly.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- May 1999
- DOI:
- 10.48550/arXiv.math/9905184
- arXiv:
- arXiv:math/9905184
- Bibcode:
- 1999math......5184Z
- Keywords:
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- Algebraic Geometry;
- Rings and Algebras;
- 16R30
- E-Print:
- 15 pages, to appear in Michigan Math. Journal