English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Moduli spaces of symmetric cubic fourfolds and locally symmetric varieties

MPS-Authors
/persons/resource/persons255487

Zheng,  Zhiwei
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (public)

arXiv:1806.04873.pdf
(Preprint), 428KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Yu, C., & Zheng, Z. (2020). Moduli spaces of symmetric cubic fourfolds and locally symmetric varieties. Algebra & Number Theory, 14(10), 2647-2683. doi:10.2140/ant.2020.14.2647.


Cite as: http://hdl.handle.net/21.11116/0000-0007-A28B-5
Abstract
In this paper we realize the moduli spaces of cubic fourfolds with specified automorphism groups as arithmetic quotients of complex hyperbolic balls or type IV symmetric domains, and study their compactifications. Our results mainly depend on the well-known works about moduli space of cubic fourfolds, including the global Torelli theorem proved by Voisin ([Voi86]) and the characterization of the image of the period map, which is given by Laza ([Laz09, Laz10]) and Looijenga ([Loo09]) independently. The key input for our study of compactifications is the functoriality of Looijenga compactifications, which we formulate in the appendix (section A). The appendix can also be applied to study the moduli spaces of singular K3 surfaces and cubic fourfolds, which will appear in a subsequent paper.