On the generalized toroidal completion of period mappings

2025/06/11 by Hao‐Hua Deng, Jacob Tsimerman, Deng, Haohua +1 · 1 citation
Computer Science · Mathematics · #14A21 #14D07 #32G20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.10109

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a period map defined over a quasi-projective variety, we construct a completion with rich geometric and Hodge-theoretic meaning. This result may be regarded as an analog of Mumford's toroidal compactification for locally symmetric Hodge varieties as well as a realizable alternative of Kato--Nakayama--Usui's construction.

Citations

• Baily--Borel compactifications of period images and the b-semiampleness conjecture
• On the generic degree of two-parameter period mappings
• Completion of two-parameter period maps by nilpotent orbits
• Hodge theory, between algebraicity and transcendence
• Extension of Period Maps by Polyhedral Fans
• Definability of mixed period maps
• o-minimal GAGA and a conjecture of Griffiths
• Tame topology of arithmetic quotients and algebraicity of Hodge loci
• Hodge loci and atypical intersections: conjectures
• Period mappings and properties of the augmented Hodge line bundle
• Polarized relations on horizontal SL(2)s
• Quotients of non-classical flag domains are not algebraic
• Determinantal Quintics and Mirror Symmetry of Reye Congruences
• Classifying spaces of degenerating mixed Hodge structures, III: Spaces of nilpotent orbits
• The Moduli Space of Cubic Threefolds as a Ball Quotient
• Torification and Factorization of Birational Maps
• On the Locus of Hodge Classes

Cited by

• Period maps at infinity

Related

• Completion of a period map of Hodge type (1,2,2,1)
• Extension of Period Maps by Polyhedral Fans
• Space of nilpotent orbits and extension of period maps (I): The weight 3 Calabi-Yau types
• A period map for global derived stacks
• Quasiprojectivity of images of mixed period maps