A survey on the Campana-Peternell Conjecture

2014/01/01 by Roberto Muñoz, Gianluca Occhetta, Luis E. Solá Conde +2
Mathematics · #Algebraic Geometry and Number Theory #Bundle #Characterization (materials science) #Combinatorics #Computer science #Conjecture #Extension (predicate logic) #Fano plane #Geometry #Geometry and complex manifolds #Homogeneous #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Projective space #Projective test #Pure mathematics #Space (punctuation) #Tangent #Tangent bundle #Tangent space #math.AG #msc:14E30 #msc:14J45 #msc:14M17

paper · pdf · doi:10.13137/0049-4704/11223

published as Rend. Istit. Mat. Univ. Trieste Volume 47 (2015), 127-185 · 47 pages

openalex publication_date 2014/01/01 · arxiv created 2015/11/11 · arxiv updated 2016/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature
• Ample Subvarieties of Algebraic Varieties
• Projective Manifolds with Ample Tangent Bundles
• Strong rigidity of positive quaternion-K�hler manifolds
• Toward a Numerical Theory of Ampleness
• Fano 5-folds with nef tangent bundles