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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


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.


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

zbMATH: 1388.14037
MathSciNet: MR3791209

Digital Object Identifier: 10.2969/aspm/07410073

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

Keywords: Relative dualizing sheaf , semiampleness , variation of Hodge structure

Rights: Copyright © 2017 Mathematical Society of Japan


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