Geometry of GLn(C) on infinity: complete collineations, projective compactifications, and universal boundary
Abstract
Consider a finite dimensional (generally reducible) polynomial representation of GLn. A projective compactification of GLn is the closure of (GLn) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GLn). 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 GLn.
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