Limiting configurations for solutions of Hitchin’s equation
Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014), pp. 91-116.

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 role is played by the family of rotationally symmetric solutions to the self-duality equation on , which we discuss in detail here.

DOI : 10.5802/tsg.296
Mazzeo, Rafe 1 ; Swoboda, Jan 2 ; Weiß, Hartmut 3 ; Witt, Frederik 4

1 Department of Mathematics Stanford University Stanford, CA 94305 (USA)
2 Mathematisches Institut der LMU München Theresienstraße 39 D–80333 München (Germany)
3 Mathematisches Seminar der Universität Kiel Ludewig-Meyn Straße 4 D–24098 Kiel (Germany)
4 Mathematisches Institut der Universität Münster Einsteinstraße 62 D–48149 Münster (Germany)
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Mazzeo, Rafe; Swoboda, Jan; Weiß, Hartmut; Witt, Frederik. Limiting configurations for solutions of Hitchin’s equation. Séminaire de théorie spectrale et géométrie, Tome 31 (2012-2014), pp. 91-116. doi : 10.5802/tsg.296. http://www.numdam.org/articles/10.5802/tsg.296/

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