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Integral Hodge classes on fourfolds fibered by quadric bundles


Authors: Zhiyuan Li and Zhiyu Tian
Journal: Proc. Amer. Math. Soc. 144 (2016), 3333-3345
MSC (2010): Primary 14C25, 14C30
DOI: https://doi.org/10.1090/proc/12999
Published electronically: March 17, 2016
MathSciNet review: 3503702
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Abstract: We discuss the space of sections and certain bisections on a quadric surfaces bundle $ X$ over a smooth curve. The Abel-Jacobi from these spaces to the intermediate Jacobian will be shown to be dominant with rationally connected fibers. As an application, we prove that the integral Hodge conjecture holds for degree $ 4$ integral Hodge classes (IHC) of fourfolds fibered by quadric bundles over a smooth curve. This gives an alternative proof of a result of Colliot-Thélène and Voisin.


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Additional Information

Zhiyuan Li
Affiliation: Mathematisches Institut, University of Bonn, Endenicher Allee 60, Bonn 53115, Germany
Email: zhiyli@math.uni-bonn.de

Zhiyu Tian
Affiliation: CNRS, Institute Fourier, UMR, 5582, 100 Rue des Mathématiques, BP 74, 38402, Saint-Martin d’Héres, France
Email: zhiyu.tian@ujf-grenoble.fr

DOI: https://doi.org/10.1090/proc/12999
Received by editor(s): November 8, 2014
Received by editor(s) in revised form: July 29, 2015, October 12, 2015, and October 18, 2015
Published electronically: March 17, 2016
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society