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The algebraic and analytic compactifications of the Hitchin moduli space
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Following the work of Mazzeo–Swoboda–Weiß–Witt [Duke Math. J. 165 (2016), 2227–2271] and Mochizuki [J. Topol. 9 (2016), 1021–1073], there is a map
$\overline{\Xi }$ between the algebraic compactification of the Dolbeault moduli space of 
${\rm SL}(2,\mathbb{C})$ Higgs bundles on a smooth projective curve coming from the 
$\mathbb{C}^\ast$ action and the analytic compactification of Hitchin’s moduli space of solutions to the 
$\mathsf{SU}(2)$ self-duality equations on a Riemann surface obtained by adding solutions to the decoupled equations, known as ‘limiting configurations’. This map extends the classical Kobayashi–Hitchin correspondence. The main result that this article will show is that 
$\overline{\Xi }$ fails to be continuous at the boundary over a certain subset of the discriminant locus of the Hitchin fibration.
