Boundedness of the images of period maps and applications

2015/06/30 by Kefeng Liu, Yang Shen, Liu, Kefeng +1
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1507.01860

openalex publication_date 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domain in a complex Euclidean space. As an application we prove that the Teichmüller spaces of a large class of projective manifolds have complex affine structures.

Citations

• From local Torelli to global Torelli

Related

• Boundedness of the Images of Period Maps
• Simultaneous normalization of period map and affine structures on moduli spaces
• Sections of Hodge bundles I: Global theory and applications to period maps
• Algebraicity of the image of period map
• Period mappings and properties of the augmented Hodge line bundle