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Jacobian rings for homogenous vector bundles and applications

An Huang Brandeis University Bong Lian Brandeis University Shing-Tung Yau Harvard University Chenglong Yu Harvard University

mathscidoc:1802.01003

2018.1
In this note, we examine the Jacobian ring description of the Hodge structure of zero loci of vector bundle sections on a class of ambient varieties. We consider a set of cohomological vanishing conditions that imply such a description, and we verify these conditions for some new cases. We also observe that the method can be directly extended to log homogeneous varieties. We apply the Jacobian ring to study the null varieties of period integrals and their derivatives, generalizing a result in [9] for projective spaces. As an additional application, we prove the Hodge conjecture for very generic hypersurfaces in certain generalized flag varieties.
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@inproceedings{an2018jacobian,
  title={Jacobian rings for homogenous vector bundles and applications},
  author={An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208152219695359919},
  year={2018},
}
An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu. Jacobian rings for homogenous vector bundles and applications. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208152219695359919.
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