Normality and smoothness of simple linear group compactifications
Algebraic Geometry
2018-06-26 v2 Representation Theory
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.
Cite
@article{arxiv.1203.1465,
title = {Normality and smoothness of simple linear group compactifications},
author = {Jacopo Gandini and Alessandro Ruzzi},
journal= {arXiv preprint arXiv:1203.1465},
year = {2018}
}
Comments
v2: minor changes, final version. To appear in Math. Z