About: Wonderful compactification

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