Open Access
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

Adv. Stud. Pure Math., 2017: 73-102 (2017) DOI: 10.2969/aspm/07410073


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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