ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES

Journal article, 2022

Let p : X → Y be an algebraic fiber space, and let L be a line bundle on. In this article, we obtain a curvature formula for the higher direct images of ΩiX/Y ⊗ L restricted to a suitable Zariski open subset of X. Our results are particularly meaningful if L is semi-negatively curved on X and strictly negative or trivial on smooth fibers of p. Several applications are obtained, including a new proof of a result by Viehweg-Zuo in the context of a canonically polarized family of maximal variation and its version for Calabi-Yau families. The main feature of our approach is that the general curvature formulas we obtain allow us to bypass the use of ramified covers - and the complications that are induced by them.