ALGEBRAIC FIBER SPACES and CURVATURE of HIGHER DIRECT IMAGES
Artikel i vetenskaplig tidskrift, 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

Författare

Bo Berndtsson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Mihai Pǎun

Universität Bayreuth

Xu Wang

Norges teknisk-naturvitenskapelige universitet

Journal of the Institute of Mathematics of Jussieu

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

Vol. In Press

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1017/S147474802000050X

Mer information

Senast uppdaterat

2020-11-05