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Séminaire de Théorie spectrale et géométrie (Grenoble)

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Rafe Mazzeo; Jan Swoboda; Hartmut Weiß; Frederik Witt
Limiting configurations for solutions of Hitchin’s equation
Séminaire de Théorie spectrale et géométrie (Grenoble), 31 (2012-2014), p. 91-116, doi: 10.5802/tsg.296
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Résumé - Abstract

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 $\mathbb{C}$, which we discuss in detail here.

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