Configurations of linear subspaces and rational invariants
Abstract
We construct a birational equivalence between certain quotients of stuples 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 stuples of linear 2planes in $C^n$ modulo the diagonal $\gl_n(C)$action . Furthermore, we compute generators of the field of the rational invariants explicitly.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 1999
 arXiv:
 arXiv:math/9905184
 Bibcode:
 1999math......5184Z
 Keywords:

 Algebraic Geometry;
 Rings and Algebras;
 16R30
 EPrint:
 15 pages, to appear in Michigan Math. Journal