Normality and smoothness of simple linear group compactifications

Details Normality and smoothness of simple linear group compactifications Normality and smoothness of simple linear group compactifications

2012-03-07

arxiv.org/abs/1203.1465v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

If G is a complex semisimple algebraic group, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant GxG-compactifications which possess a unique closed orbit and which arise in a projective space of the shape P(End(V)), where V is finitely dimensional rational G-module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of V. In particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple group which admits a simple smooth compactification.

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