Nonlinear Harmonic Bundles

2025/12/04 by Sheng Mao, Sheng, Mao
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2512.04809

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

Abstract

We generalize the notion of harmonic bundles in nonabelian Hodge theory to the nonlinear setting.

Citations

• Nonabelian Kodaira-Spencer maps
• Nonabelian Hodge Theory in Characteristic p
• The Hodge filtration on nonabelian cohomology
• The Self-Duality Equations on a Riemann Surface

Related

• Nonlinear Hodge equations in vector bundles
• Nonlinear Hodge correspondence in positive characteristic
• Loop Hodge structure and harmonic bundles
• Hodge Theory and Higgs Bundle on Moduli Spaces of Smooth Varieties with Semi-Ample Canonical Line Bundles, Negativity and Hyperbolicity
• Harmonic Bundles with Symplectic Structures