Poisson Structures on Moduli Spaces of Higgs Bundles over Stacky Curves

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.

arXiv comment20 pages

References in corpus (8)

• Quasi-Hamiltonian Geometry of Meromorphic Connections
• Orbifold Riemann Surfaces and the Yang-Mills-Higgs Equations
• Grothendieck Duality for Deligne-Mumford Stacks
• Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves
• Fibrés paraboliques et champ des racines
• Lie Algebroids over Differentiable Stacks
• The Beauville-Narasimhan-Ramanan correspondence for twisted Higgs $V$-bundles and components of parabolic $\text{Sp}(2n,\mathbb{R})$-Higgs moduli Spaces
• Moduli Problem of Hitchin Pairs over Deligne-Mumford Stack