论文标题
Fano变形下出色的团体压缩的刚度
Rigidity of wonderful group compactifications under Fano deformations
论文作者
论文摘要
对于复杂的连接的半神经线性代数组$ g $的伴随类型和等级$ n $，de concini和procesi构建了其出色的紧凑型$ \ bar {g} $，这是一种平稳的fano $ g \ times g \ times g $ g $ g $ - picard n $ n $ n $享受许多有趣的属性。在本文中，显示出奇妙的紧凑型$ \ bar {g} $在Fano变形下是刚性的。也就是说，对于连接底座上的任何常规Fano歧管家庭，如果一种纤维是同构成$ \ bar {g} $的，那么所有其他纤维也是如此。这回答了Bien和Brion在他们关于奇妙品种的当地刚性方面提出的一个问题。
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.
