Limiting configurations for solutions of Hitchin's equation

We review recent work on the compactification of the moduli space of Hitchin's self-duality equation. We study the degeneration behavior near the ends of this moduli space in a set of generic directions by showing how limiting configurations can be desingularized. Following ideas of Hitchin, we can relate the top boundary stratum of this space of limiting configurations to a Prym variety. A key rôle is played by the family of rotationally symmetric solutions to the self-duality equation on $\mathbb C$, which we discuss in detail here.

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