Normality and smoothness of simple linear group compactifications

Abstract

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 finite 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.

v2: minor changes, final version. To appear in Math. Z

References in corpus (2)

• Normality and non-normality of group compactifications in simple projective spaces
• Simple linear compactifications of odd orthogonal groups

Cited by in corpus (2)

• Kähler-Einstein metrics on group compactifications
• Simple linear compactifications of odd orthogonal groups