On Fano complete intersections in rational homogeneous varieties

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 $K_{G/P}^{\ast }\otimes {\mathcal{O}}_{G/P}(-{\sum }_i{D}_i)$ 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.

References in corpus (1)

• On linear sections of the spinor tenfold, I

Cited by in corpus (3)

• The double Cayley Grassmannian
• On the deformation rigidity of smooth projective symmetric varieties with Picard number one
• Topics on the geometry of homogeneous spaces