On Fano complete intersections in rational homogeneous varieties

Chenyu Bai , Baohua Fu , Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if X = ∩ r i=1 D i ⊂ G/P is a general complete intersection of r ample divisors such that 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.

Domaines: Mathématiques [math]; Géométrie algébrique [math.AG]

Chenyu Bai, Baohua Fu, Laurent Manivel. On Fano complete intersections in rational homogeneous varieties. Mathematische Zeitschrift, 2020, 295, pp.289-308. ⟨hal-01968757⟩