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Register a new userRigidity of wonderful group compactifications under Fano deformations
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For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification bar{G}, which is a smooth Fano G times G-variety of Picard number n enjoying many interesting properties. In this paper, it is shown that the wonderful compactification bar{G} is rigid under Fano deformations. Namely, for any family of smooth Fano varieties over a connected base, if one fiber is isomorphic to bar{G}, then so are all other fibers.
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Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an application, we show that X has the target rigidity property when G is not of type A_1 or C.
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