B. Berndtsson - The curvature of (higher) direct images

Bo Berndtsson (1) , Jérémy Magnien (2)

1 Department of Mathematical Sciences
2 IF - Institut Fourier

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.)

Mots clés: Complex analytic and differential geometry 2017; curvature; Grenoble; images

Domaines: Géométrie différentielle [math.DG]

Bo Berndtsson, Jérémy Magnien. B. Berndtsson - The curvature of (higher) direct images: Complex analytic and differential geometry 2017. 2017. ⟨medihal-01614938⟩