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Period integrals of vector bundle sections and tautological systems

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

Algebraic Geometry mathscidoc:2206.45005

Mathematical Research Letters, 28, (2), 415-434, 2021.5
Tautological systems developed in [8, 9] are Picard-Fuchs type systems to study period integrals of complete intersections in Fano varieties. We generalize tautological systems to zero loci of global sections of vector bundles. In particular, we obtain similar criterion as in [8, 9] about holonomicity and regularity of the systems. We also prove solution rank formulas and geometric realizations of solutions following the work on hypersurfaces in homogeneous varieties [4].
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@inproceedings{an2021period,
  title={Period integrals of vector bundle sections and tautological systems},
  author={An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618171613927660417},
  booktitle={Mathematical Research Letters},
  volume={28},
  number={2},
  pages={415-434},
  year={2021},
}
An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu. Period integrals of vector bundle sections and tautological systems. 2021. Vol. 28. In Mathematical Research Letters. pp.415-434. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618171613927660417.
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