Moduli Spaces of Homologically Trivial Parabolic (Higgs) Bundles on the Projective Line and an Application to the Deligne-Simpson Problem

Abstract

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on ${\mathbb{P}}^1$ and the quiver variety associated to a star-shaped quiver. As an application, we give a Hitchin-theoretic construction of irreducible solutions to the nilpotent additive Deligne-Simpson problem under explicit numerical assumptions.

References in corpus (6)

• Lectures on Nakajima's Quiver Varieties
• Degeneration of moduli spaces and generalized theta functions
• Hyperpolygons and Hitchin systems
• Parabolic Hitchin Maps and Their Generic Fibers
• Symplectic form on hyperpolygon spaces
• Globally F-regular type of moduli spaces and Verlinde formula

Cited by in corpus (2)

• Integrable systems on multiplicative quiver varieties from cyclic quivers
• A closed formula of Littlewood-Richardson coefficients