2018/08/05 by Chenyu Bai, Bai, Chenyu, Fu, Baohua +2 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.1808.01549
Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if X = ∩i=1r Di ⊂ G/P is a general complete intersection of r ample divisors such that KG/P^* ⊗ OG/P(-∑i Di) 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.