Manifolds with two projective bundle structures

Abstract

In this paper we classify varieties of Picard number two having two projective bundle structures of any relative dimension, under the assumption that these structures are mutually uniform. As an application we prove the Campana--Peternell conjecture for varieties of Picard number one admitting ${\mathbb{C}}^{\ast }$-actions of a certain kind.

arXiv comment15 pages

References in corpus (4)

• On uniform flag bundles on Fano manifolds
• Smooth projective horospherical varieties with nef tangent bundles
• Adjunction for varieties with a ${\mathbb{C}}^{\ast }$ action
• Nestings of rational homogeneous varieties

Cited by in corpus (2)

• The generalized roof F(1,2,n): Hodge structures and derived categories
• Calabi-Yau fibrations, simple K-equivalence and mutations