Wonderful compactification explained

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 ^{\sigma} of an algebraic group G by the subgroup G ^{\sigma} 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 x G)/G (modulo the diagonal subgroup), this gives a wonderful compactification of the group G itself.

References

• • • Li. Li. Wonderful compactification of an arrangement of subvarieties. Michigan Mathematical Journal. 58 . 2009. 2. 535–563. 2595553. 10.1307/mmj/1250169076. math/0611412. 119637721.