  In this note we study some analytic properties of the linearized self-duality
equations on a family of smooth Riemann surfaces $\Sigma_R$ converging for
$R\searrow0$ to a surface $\Sigma_0$ 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.
