Translator Disclaimer
VOL. 74 | 2017 Answer to a question by Fujita on Variation of Hodge Structures
Fabrizio Catanese, Michael Dettweiler

Editor(s) Keiji Oguiso, Caucher Birkar, Shihoko Ishii, Shigeharu Takayama

Abstract

We first provide details for the proof of Fujita's second theorem for Kähler fibre spaces over a curve, asserting that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. Our main result then answers in the negative the question posed by Fujita whether $V$ is semiample. In fact, $V$ is semiample if and only if $Q$ is associated to a representation of the fundamental group of $B$ having finite image. Our examples are based on hypergeometric integrals.

Information

Published: 1 January 2017
First available in Project Euclid: 23 October 2018

zbMATH: 1388.14037
MathSciNet: MR3791209

Digital Object Identifier: 10.2969/aspm/07410073

Subjects:
Primary: 14C30, 14D07, 32G20, 33C60

Rights: Copyright © 2017 Mathematical Society of Japan

PROCEEDINGS ARTICLE
30 PAGES


SHARE
RIGHTS & PERMISSIONS
Get copyright permission
Back to Top