Integral Hodge classes on fourfolds fiberd by quadric bundles

Zhiyuan Li; Zhiyu Tian

Integral Hodge classes on fourfolds fiberd by quadric bundles

Algebraic Geometry 2014-11-03 v3

Authors: Zhiyuan Li , Zhiyu Tian

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 four integral Hodge classes of fourfolds fibered by quadric bundles over a smooth curve. This gives an alternative proof of a result of Colliot-Th{\'e}l{\`e}ne and Voisin.

Keywords

integral hodge conjecture quadric bundles fourfolds abel-jacobi map intermediate jacobian rationally connected fibers

Cite

@article{arxiv.1402.6051,
  title  = {Integral Hodge classes on fourfolds fiberd by quadric bundles},
  author = {Zhiyuan Li and Zhiyu Tian},
  journal= {arXiv preprint arXiv:1402.6051},
  year   = {2014}
}

Comments

As we think that our geometric approach might still be interesting, we make it available. There will be a future work related to this paper. Some typos have been fixed

Integral Hodge classes on fourfolds fiberd by quadric bundles

Abstract

Keywords

Cite

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