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 ( 1983) 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 ( 1987) 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.
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 ( 1983) 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 ( 1987) 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.