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Configurations of linear subspaces and rational invariants

Dmitri Zaitsev
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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.

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Dmitri Zaitsev. 1999-05-29. Configurations of linear subspaces and rational invariants. https://arxiv.org/abs/math/9905184

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