نبذة مختصرة : 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.)
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