Wonderful compactification
In algebraic group theory, a wonderful compactification of a variety acted on by an algebraic group G {\displaystyle G} is a G {\displaystyle G} -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 G / G σ {\displaystyle G/G^{\sigma }} of an algebraic group G {\displaystyle G} by the subgroup G σ {\displaystyle G^{\sigma }} fixed by some involution σ {\displaystyle \sigma } of G {\displaystyle G} over the complex numbers, sometimes called the De Concini–Procesi compactification.
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