Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary
arXiv:math/0012206 · doi:10.1007/978-1-4612-0029-1_13
Abstract
Consider a finite dimensional (generally reducible) polynomial representation ρof GL_n. A projective compactification of GL_n is the closure of ρ(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.
24 pages, corrected variant