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  Moduli spaces of symmetric cubic fourfolds and locally symmetric varieties

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.

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 Creators:
Yu, Chenglong, Author
Zheng, Zhiwei1, Author              
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry
 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Published in print
 Pages: 37
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1806.04873
DOI: 10.2140/ant.2020.14.2647
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Title: Algebra & Number Theory
Source Genre: Journal
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Publ. Info: Mathematical Sciences Publishers
Pages: - Volume / Issue: 14 (10) Sequence Number: - Start / End Page: 2647 - 2683 Identifier: -