Paper detail

The Hitchin fibration under degenerations to noded Riemann surfaces

In this note we study some analytic properties of the linearized self-duality equations on a family of smooth Riemann surfaces $Σ_R$ converging for $R\searrow0$ to a surface $Σ_0$ with a finite number of nodes. It is shown that the linearization along the fibres of the Hitchin fibration gives rise to a graph-continuous Fredholm family, the index of it being stable when passing to the limit. We also report on similarities and differences between properties of the Hitchin fibration in this degeneration and in the limit of large Higgs fields.