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Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties

Chenglong Yu University of Pennsylvania, Philadelphia, PA, United States Zhiwei Zheng Max Planck Institute for Mathematics, Bonn, Germany

Algebraic Geometry mathscidoc:2206.45001

Algebra & Number Theory, 14, (10), 2647–2683, 2020.11
We realize the moduli spaces of cubic fourfolds with specified group actions as arithmetic quotients of complex hyperbolic balls or type IV symmetric domains, and study their compactifications. We prove the geometric (GIT) compactifications are naturally isomorphic to the Hodge theoretic (Looijenga, in many cases Baily–Borel) compactifications. The key ingredients of the proof are the global Torelli theorem by Voisin, the characterization of the image of the period map given by Looijenga and Laza independently, and the functoriality of Looijenga compactifications proved in the Appendix.
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@inproceedings{chenglong2020moduli,
  title={Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties},
  author={Chenglong Yu, and Zhiwei Zheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618165258162612413},
  booktitle={Algebra & Number Theory},
  volume={14},
  number={10},
  pages={2647–2683},
  year={2020},
}
Chenglong Yu, and Zhiwei Zheng. Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties. 2020. Vol. 14. In Algebra & Number Theory. pp.2647–2683. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618165258162612413.
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