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A REMARK ON FUJINO’S WORK ON THE CANONICAL BUNDLE FORMULA VIA PERIOD MAPS

Part of: Families, fibrations Birational geometry Cycles and subschemes Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  02 December 2024

HYUNSUK KIM Open the ORCID record for HYUNSUK KIM [Opens in a new window]
HYUNSUK KIM*
Affiliation:
Department of Mathematics University of Michigan, Ann Arbor 530 Church Street Ann Arbor, Michigan United States
*
[email protected]
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Abstract

Fujino gave a proof for the semi-ampleness of the moduli part in the canonical bundle formula in the case when the general fibers are K3 surfaces or abelian varieties. We show a similar statement when the general fibers are primitive symplectic varieties. This answers a question of Fujino raised in the same article. Moreover, using the structure theory of varieties with trivial first Chern class, we reduce the question of semi-ampleness in the case of families of K-trivial varieties to a question when the general fibers satisfy a slightly weaker Calabi–Yau condition.

Keywords

canonical bundle formulaperiod mapsminimal model program

MSC classification

Primary: 14C30: Transcendental methods, Hodge theory , Hodge conjecture 14D07: Variation of Hodge structures 14E30: Minimal model program (Mori theory, extremal rays) 14J27: Elliptic surfaces
Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 14
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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