Abstract
Let
$p:X\rightarrow Y$
be an algebraic fiber space, and let
$L$
be a line bundle on
$X$
. In this article, we obtain a curvature formula for the higher direct images of
$\unicode[STIX]{x1D6FA}_{X/Y}^{i}\otimes L$
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.
Publisher
Cambridge University Press (CUP)
Reference49 articles.
1. On the negativity of kernels of Kodaira–Spencer maps on Hodge bundles and applications
2. 48. Yoshikawa, K.-I. , to appear.
3. Hodge metrics and positivity of direct images;Mourougane;J. Reine Angew. Math.,2007
4. 8. Cao, J. and Păun, M. , Kodaira dimension of algebraic fiber spaces over abelian varieties, Invent. Math. (2017) Preprint, 2015, arXiv:1504.01095.
5. On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
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