Related papers: Subharmonicity of direct images and applications
We consider a holomorphic family $f:\mathcal{X} \to S$ of compact complex manifolds and a line bundle $\mathcal{L}\to \mathcal{X}$. Given that $\mathcal{L}^{-1}$ carries a singular hermitian metric that has Poincar\'e type singularities…
In this paper we consider various notions of positivity for distributions on complex projective manifolds. We start by analyzing distributions having big slope with respect to curve classes, obtaining characterizations of generic projective…
In this note we extend connectedness results to formal properties of inverse images under proper maps of Schubert varieties and of the diagonal in products of projective rational homogeneous spaces
We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…
It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, vanishing of higher cohomology leading to existence of global…
We give applications of the higher Lefschetz theorems for foliations of [BH10], primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information.…
Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature.…
We extend the notion of topological T-duality from oriented sphere bundles to transgressive fibrations, a more general type fibration characterised by the abundance of transgressive elements. Examples of transgressive fibrations include…
In previous work, we have introduced delta-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern delta-forms. In this paper, we investigate positivity properties…
This paper is a sequel to \cite{Berndtsson}. In that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth K\"ahler morphism, twisted with a semipositive line bundle. We proved that…
Let $\pi:\mathcal{X}\to M$ be a holomorphic fibration with compact fibers and $L$ a relatively ample line bundle over $\mathcal{X}$. We obtain the asymptotic of the curvature of $L^2$-metric and Qullien metric on the direct image bundle…
Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family $H_s$ of Hilbert spaces, and the question arises if the spaces $H_s$ are canonically isomorphic. [ADW] and…
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic…
We examine various aspects of the conjectured duality between warped AdS$_5$ geometries with boundary branes and strongly coupled (broken) conformal field theories coupled to dynamical gravity. We also examine compactifications with 5-d…
The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to…
In a previous paper, \cite{Berndtsson}, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted $L^2$-spaces of holomorphic functions. Here we prove a result on the curvature of a…
We give a "conceptual" approach to Kourganoff's results about foliations with a transverse similarity structure. In particular, we give a proof, understandable by the targeted community, of the very important result classifying the holonomy…
In this paper, we study the twisted basic Dolbeault cohomology and transverse hard Lefschetz theorem on a transverse Kahler foliation. And we give some properties for $\Delta_\kappa$-harmonic forms and prove the Kodaira-Serre type duality…