Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary
Representation Theory
2013-01-15 v2 Algebraic Geometry
Differential Geometry
Rings and Algebras
Abstract
Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(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.
Keywords
Cite
@article{arxiv.math/0012206,
title = {Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary},
author = {Yurii A. Neretin},
journal= {arXiv preprint arXiv:math/0012206},
year = {2013}
}
Comments
24 pages, corrected variant