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arXiv · 1808.01549

On Fano complete intersections in rational homogeneous varieties

Chenyu Bai·Baohua Fu·Laurent Manivel
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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 general 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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Chenyu Bai, Baohua Fu, Laurent Manivel. 2018-08-05. On Fano complete intersections in rational homogeneous varieties. https://arxiv.org/abs/1808.01549

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