The curvature of (higher) direct images

curvature
grenoble
Complex analytic and differential geometry 2017
images
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]

I will first discuss some earlier work on the curvature of direct images of adjoint line bundles under a smooth proper fibration, or more generally a surjective map and (maybe) some of its applications. Then I will present a general formula for the curvature of higher direct images. This contains as a special case (part of) the earlier work, and also generalizes results of Siu and Schumacher. (The second part is based on joint work with Mihai Paun and Xu Wang.)