Abstract
Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if \(X = \cap _{i=1}^r D_i \subset G/P\) is a smooth complete intersection of r ample divisors such that \(K_{G/P}^* \otimes {\mathcal O}_{G/P}(-\sum _i D_i)\) 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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Acknowledgements
We are grateful to Michel Brion for Lemma 3.3 and for the reference [21]. Baohua Fu is supported by National Natural Science Foundation of China (nos. 11431013, 11688101 and 11771425). Part of this work is done during the visit of Baohua Fu to the CMSA of Harvard University and he would like to thank the CMSA for the hospitality. We would like to thank the referee for numerous suggestions.
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Bai, C., Fu, B. & Manivel, L. On Fano complete intersections in rational homogeneous varieties. Math. Z. 295, 289–308 (2020). https://doi.org/10.1007/s00209-019-02351-4
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DOI: https://doi.org/10.1007/s00209-019-02351-4