Normality and non-normality of group compactifications in simple projective spaces

Abstract

If $G$ is a complex simply connected semisimple algebraic group and if $\lambda$ is a dominant weight, we consider the compactification $X_{\lambda }$ in the projectivisation of $\End(V(λ))$ obtained as the closure of the $G\times G$-orbit of the identity and we give necessary and sufficient conditions on the support of $\lambda$ so that $X_{\lambda }$ is normal; as well, we give necessary and sufficient conditions on the support of $\lambda$ so that $X_{\lambda }$ is smooth.

v2: minor changes, final version to appear in Ann. Inst. Fourier (Grenoble)

References in corpus (1)

• Smooth Projective Symmetric Varieties with Picard Number equal to one

Cited by in corpus (3)

• Projective normality of model varieties and related results
• Normality and smoothness of simple linear group compactifications
• Simple linear compactifications of odd orthogonal groups