The moduli space of cubic fourfolds via the period map

• 成果类型: Article
• 署名作者: Laza, Radu
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.673
• 发表日期: 2010
• 页码: 673-711
• 关键词: torelli theorem; k3 surfaces; hypersurfaces; SINGULARITIES; threefolds; VARIETIES; conjecture; steenbrink; versality; families

摘要

We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the geometric invariant theory (GIT) compactification of the moduli space of cubic fourfolds is isomorphic to the Looijenga compactification associated to this arrangement. This paper builds on and is a natural continuation of our previous work on the GIT compactification of the moduli space of cubic fourfolds.