Moduli spaces of Higgs bundles on degenerating Riemann surfaces

TL;DR

This paper establishes a gluing theorem for solutions to Hitchin's self-duality equations with singularities on degenerating Riemann surfaces, advancing understanding of moduli spaces in complex geometry.

Contribution

It introduces a novel gluing technique for Higgs bundle solutions on noded surfaces, connecting degenerating geometries with smooth moduli space structures.

Findings

Proved a gluing theorem for Higgs bundle solutions on noded surfaces.

Connected solutions on degenerating surfaces to smooth moduli spaces.

Enhanced understanding of Higgs bundle behavior near boundary points.

Abstract

We prove a gluing theorem for solutions of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface representing a boundary point of Teichm\"uller moduli space.