Rationally connected manifolds and semipositivity of the Ricci curvature
By Frédéric Campana, J. Demailly, T. Peternell. 2012
63 citations recorded by the source corpus.
This work establishes a structure theorem for compact Kahler manifolds with semipositive anticanonical bundle. Up to finite etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat varieties and of rationally connected manifolds. The proof is based on a characterization of rationally connected manifolds through the non existence of certain twisted contravariant tensor products of the tangent bundle, along with a generalized holonomy principle for pseudoeffective line bundles. A crucial ingredient for this is the characterization of uniruledness by the property that the anticanonical bundle is not pseudoeffective.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/53a8b5084b3bcfac7ba99d1b763b1abd016bafdb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A decomposition theorem for projective manifolds with nef anticanonical bundle (2017, background): “This conjecture has been proven under the stronger assumption that T X is nef [CP91, DPS94], − K X is hermitian semipositive [DPS96, CDP15] or the general fibre of the Albanese map is weak Fano [CH17].”
- RC-positivity, rational connectedness and Yau's conjecture (2017, background): “5 can also be implied by the “Generalized holonomy principle” for positive curvature and the main theorem in [12], although the precise result is not stated there.”