Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $$X = \cap _{i=1}^r D_i \subset G/P$$ X = ∩ i = 1 r D i ⊂ G / P is a smooth complete intersection of r ample divisors such that $$K_{G/P}^* \otimes {\mathcal O}_{G/P}(-\sum _i D_i)$$ K G / P ∗ ⊗ O G / P ( - ∑ i D i ) is ample, then X is Fano. We first classify these Fano complete intersections which are locally rigid. It turns out that most of them are hyperplane sections. We then classify general hyperplane sections which are quasi-homogeneous.

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关于有理同质簇中的 Fano 完全交集

有理齐种内的完全交集提供了有趣的 Fano 流形示例。例如，如果 $$X = \cap _{i=1}^r D_i \subset G/P$$ X = ∩ i = 1 r D i ⊂ G / P 是 r 个充足因数的平滑完全交集，使得$$K_{G/P}^* \otimes {\mathcal O}_{G/P}(-\sum _i D_i)$$ KG / P ∗ ⊗ OG / P ( - ∑ i D i ) 是充足的，那么X就是法诺。我们首先对这些局部刚性的 Fano 完全交叉点进行分类。事实证明，它们中的大多数是超平面截面。然后我们对准齐次的一般超平面部分进行分类。