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For a complex connected semisimple linear algebraic group $G$ of adjoint typeand of rank $n$, De Concini and Procesi constructed its wonderfulcompactification $\bar{G}$, which is a smooth Fano $G \times G$-variety ofPicard number $n$ enjoying many interesting properties. In this paper, it isshown that the wonderful compactification $\bar{G}$ is rigid under Fanodeformation. Namely, for any regular family of Fano manifolds over a connectedbase, if one fiber is isomorphic to $\bar{G}$, then so are all other fibers.This answers a question raised by Bien and Brion in their work on the localrigidity of wonderful varieties.

Rigidity of wonderful group compactifications under Fano deformations