Hodge metrics and positivity of direct images

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle $E$ on a complex manifold, and every positive integer $k$, the vector bundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.Comment: revised and expanded version of "A positivity property of ample vector bundles

Birational geometry of hypersurfaces in products of projective spaces

We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in Pm x Pn, we describe their nef, movable and e ective cones and determine when they are Mori dream spaces. Using this, we give new simple examples of non-Mori dream spaces and analogues of Mumford's example of a strictly nef line bundle which is not ample.This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s00209-015-1415-

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Can confidence indicators be useful to predict short term real GDP growth?

We investigate the usefulness of the European Commission confidence indicators for forecasting real GDP growth rates in the short run is investigated in selected euro area countries (Belgium, Spain, Germany, France, Italy and the Netherlands) which account for almost 90% of the euro area. A linear relationship between real GDP and confidence indicators is estimated and the forecasting performance of the estimated models compared with a benchmark ARIMA model. It is generally found that confidence indicators can be useful for forecasting real GDP growth rates in the short-run in most of the above-mentioned countries. Notwithstanding some signs of instability in the relation between confidence indicators and real GDP, improvements with the use of time-varying parameter models appear to be fairly limited but confirm the findings obtained with constant parameter techniques. The results obtained are robust to a wide range of variant tests implemented.