Rigidity of wonderful group compactifications under Fano deformations

Baohua Fu; Qifeng Li

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arXiv · 2007.00275

Rigidity of wonderful group compactifications under Fano deformations

Baohua Fu·Qifeng Li

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Abstract

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 deformation. Namely, for any regular family of Fano manifolds over a connected base, 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 local rigidity of wonderful varieties.

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Baohua Fu, Qifeng Li. 2020-07-01. Rigidity of wonderful group compactifications under Fano deformations. https://arxiv.org/abs/2007.00275

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