Poisson Structures on Moduli Spaces of Higgs Bundles over Stacky Curves

2020/08/28 by Georgios Kydonakis, Hao Sun, Kydonakis, Georgios +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2008.12518

openalex publication_date 2020/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate the construction of Poisson structures via Lie algebroids on moduli spaces of twisted stable Higgs bundles over stacky curves. The construction provides new examples of Poisson structures on such moduli spaces. Special attention is paid at moduli spaces of parabolic Higgs bundles over a root stack.

Citations

• The Self-Duality Equations on a Riemann Surface
• Lie Algebroids over Differentiable Stacks
• The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs V-bundles and components of parabolic Sp(2n,ℝ)-Higgs moduli Spaces
• Moduli Problem of Hitchin Pairs over Deligne-Mumford Stack

Cited by

• Level structures on parahoric torsors and complete integrability

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• The Orbit Type Stratification OF the Moduli Space of Higgs Bundles
• Bosonization of Feigin-Odesskii Poisson varieties