Wonderful Compactification

In algebraic group theory, a wonderful compactification of a variety acted on by an algebraic group $G$ is a $G$-equivariant compactification such that the closure of each orbit is smooth. constructed a wonderful compactification of any symmetric variety given by a quotient $G/G^$ of an algebraic group $G$ by the subgroup $G^$ fixed by some involution $\sigma$ of $G$ over the complex numbers, sometimes called the De Concini–Procesi compactification, and generalized this construction to arbitrary characteristic. In particular, by writing a group $G$ itself as a symmetric homogeneous space, $G=(G \times G)/G$ (modulo the diagonal subgroup), this gives a wonderful compactification of the group $G$ itself.

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Algebraic groups
Compactification (mathematics)

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