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.

• de Concini, Corrado; Procesi, Claudio (1983), "Complete symmetric varieties", in Gherardelli, Francesco (ed.), Invariant theory (Montecatini, 1982), Lecture Notes in Mathematics, vol. 996, Berlin, New York: Springer-Verlag, pp. 1–44, doi:10.1007/BFb0063234, ISBN 978-3-540-12319-4, MR 0718125
• Evens, Sam; Jones, Benjamin F. (2008), On the wonderful compactification, Lecture notes, arXiv:0801.0456, Bibcode:2008arXiv0801.0456E
• Li, Li (2009). "Wonderful compactification of an arrangement of subvarieties". Michigan Mathematical Journal. 58 (2): 535–563. arXiv:math/0611412. doi:10.1307/mmj/1250169076. MR 2595553. S2CID 119637721.
• Springer, Tonny Albert (2006), "Some results on compactifications of semisimple groups", International Congress of Mathematicians. Vol. II, Zürich: European Mathematical Society, pp. 1337–1348, MR 2275648
• Strickland, Elisabetta (1987), "A vanishing theorem for group compactifications", Mathematische Annalen, 277 (1): 165–171, doi:10.1007/BF01457285, ISSN 0025-5831, MR 0884653, S2CID 121180091