A survey on the Campana-Peternell Conjecture

Abstract

In 1991 Campana and Peternell proposed, as a natural algebro-geometric extension of Mori's characterization of the projective space, the problem of classifying the complex projective Fano manifolds whose tangent bundle is nef, conjecturing that the only varieties satisfying these properties are rational homogeneous. In this paper we review some background material related to this problem, with special attention to the partial results recently obtained by the authors.

47 pages

References in corpus (3)

• Fano manifolds whose elementary contractions are smooth ${\mathbb{P}}^1$-fibrations: A geometric characterization of flag varieties
• Fano 5-folds with nef tangent bundles
• Uniform families of minimal rational curves on Fano manifolds

Cited by in corpus (10)

• On projective manifolds with pseudo-effective tangent bundle
• Fano n-folds with nef tangent bundle and Picard number greater than n-5
• On the Structure of Hermitian Manifolds with Semipositive Griffiths Curvature
• Smooth projective horospherical varieties with nef tangent bundles
• Uniform families of minimal rational curves on Fano manifolds
• Deformation of Bott-Samelson varieties and variations of isotropy structures
• $L^2$-extension theorems for jet sections of nef holomorphic vector bundles on compact Kähler manifolds and rational homogeneous manifolds, I
• A Characterization of Symplectic Grassmannians
• Belyi's theorem for smooth complete intersections of general type in generalised Grassmannians and weighted projective spaces
• Chern numbers on positive vector bundles and combinatorics