ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES
Journal article, 2020

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.

Posititivity

Higher direct imags of relative canonical bundle

Curvture

Singular metrics

Hodge theory

Author

Bo Berndtsson

Chalmers, Mathematical Sciences, Algebra and geometry

Mihai Pǎun

University of Bayreuth

Xu Wang

Norwegian University of Science and Technology (NTNU)

Journal of the Institute of Mathematics of Jussieu

1474-7480 (ISSN) 1475-3030 (eISSN)

Vol. In Press

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1017/S147474802000050X

More information

Latest update

11/5/2020