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

Abstract

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.

Citation

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Chenglong Yu. Zhiwei Zheng. "Moduli spaces of symmetric cubic fourfolds and locally symmetric varieties." Algebra Number Theory 14 (10) 2647 - 2683, 2020. https://doi.org/10.2140/ant.2020.14.2647

Information

Received: 4 May 2019; Revised: 14 April 2020; Accepted: 4 June 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190414
Digital Object Identifier: 10.2140/ant.2020.14.2647

Subjects:
Primary: 14D23
Secondary: 14D07

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 10 • 2020
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