Limiting configurations for solutions of Hitchin’s equation

Rafe Mazzeo[1]; Jan Swoboda[2]; Hartmut Weiß[3]; Frederik Witt[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)

Séminaire de théorie spectrale et géométrie (2012-2014)

  • Volume: 31, page 91-116
  • ISSN: 1624-5458

Abstract

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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 ℂ , which we discuss in detail here.

How to cite

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Mazzeo, Rafe, et al. "Limiting configurations for solutions of Hitchin’s equation." Séminaire de théorie spectrale et géométrie 31 (2012-2014): 91-116. <http://eudml.org/doc/275685>.

@article{Mazzeo2012-2014,
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.},
affiliation = {Department of Mathematics Stanford University Stanford, CA 94305 (USA); Mathematisches Institut der LMU München Theresienstraße 39 D–80333 München (Germany); Mathematisches Seminar der Universität Kiel Ludewig-Meyn Straße 4 D–24098 Kiel (Germany); Mathematisches Institut der Universität Münster Einsteinstraße 62 D–48149 Münster (Germany)},
author = {Mazzeo, Rafe, Swoboda, Jan, Weiß, Hartmut, Witt, Frederik},
journal = {Séminaire de théorie spectrale et géométrie},
language = {eng},
pages = {91-116},
publisher = {Institut Fourier},
title = {Limiting configurations for solutions of Hitchin’s equation},
url = {http://eudml.org/doc/275685},
volume = {31},
year = {2012-2014},
}

TY - JOUR
AU - Mazzeo, Rafe
AU - Swoboda, Jan
AU - Weiß, Hartmut
AU - Witt, Frederik
TI - Limiting configurations for solutions of Hitchin’s equation
JO - Séminaire de théorie spectrale et géométrie
PY - 2012-2014
PB - Institut Fourier
VL - 31
SP - 91
EP - 116
AB - 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.
LA - eng
UR - http://eudml.org/doc/275685
ER -

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