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 C * -actions of a certain kind.

The generalized roof F(1,2,n): Hodge structures and derived categories

“…The existence of two different projective bundle structures on a Fano variety has recently raised attention: in [ORS20] a link with the Campana-Peternell conjecture has been highlighted, while in [Kan18] the study of a broad class of K-equivalences has been reduced to the classification of roofs of projective bundles, i.e. special Fano varieties of Picard rank two which admit two different projective bundle structures of the same rank.…”

Calabi-Yau fibrations, simple K-equivalence and mutations

“…Homogeneous roof bundles. While the problem of describing and classifying families of roofs over a smooth projective variety has been addressed in [Kan18,ORS20], we focus on a special class of such families, which we call roof bundles. These objects provide a natural relativization of homogeneous roofs of projective bundles, and retain many of the properties of the latter objects in a relative setting.…”