Configurations of linear subspaces and rational invariants

Details Configurations of linear subspaces and rational invariants Configurations of linear subspaces and rational invariants

1999-05-29

arxiv.org/abs/math/9905184v1

Mathematics

Algebraic Geometry

15 pages, to appear in Michigan Math. Journal

Scientific paper

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.

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