Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

Abstract

Let $X$ be an $n$-dimensional complex Fano manifolds $(n\ge 3)$. Assume that $X$ contains a divisor $A$, which is isomorphic to a rational homogeneous space with Picard number one, such that the conormal bundle ${\mathcal{N}}_{A/X}^{\ast }$ is ample over $A$. Building on the works of Tsukioka, Watanabe and Casagrande-Druel, we give a complete classification of such pairs $(X,A)$.

This the second part of the previous preprint version and it is publised in [Internat. J. Math., 2020, 31, 2050066, 14]. However, there was one case missed in the statement of Theorem 1.2 in the publised version. We add an appendix to make a correction in this updated version

References in corpus (4)

• On linear sections of the spinor tenfold, I
• Fano manifolds having (n-1,0)-type extremal rays with large Picard number
• Projective manifolds whose tangent bundle contains a strictly nef subsheaf
• Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

Cited by in corpus (1)

• Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one