Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface

Konno, Hiroshi

doi:10.2969/jmsj/04520253

Cited by 85 publications

(136 citation statements)

References 17 publications

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“…In fact, our stability condition depends on the parameter δ 1 while the usual stability condition used in [5,16] has no parameter dependence. This is not surprising, as the stability condition of (non-parabolic) Hitchin pairs was recovered as the asymptotic stability of swamps in Section 3.6 of [12].…”

Section: Definition 34mentioning

confidence: 99%

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Stable parabolic Higgs bundles as asymptotically stable decorated swamps

Beck

2016

Journal of Geometry and Physics

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Abstract. Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behavior of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such that stability with respect to parameters greater than this constant is equivalent to asymptotic stability. This implies boundedness of all decorated swamps which are semistable with respect to some parameter. Finally, we recover the usual stability condition of parabolic Higgs bundles as asymptotic stability.

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Section: Definition 34mentioning

confidence: 99%

“…(ii) Our notion of stability of parabolic Hitchin pairs, induced by the asymptotic stability of decorated swamps, reproduces the usual stability condition for parabolic Higgs bundles as given in Definition 1.2 in [5] or Definition 1.3 in [16].…”

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confidence: 99%

Stable parabolic Higgs bundles as asymptotically stable decorated swamps

Beck

2016

Journal of Geometry and Physics

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“…Just as in the unramified case [21], or the tamely ramified case [34], [27], the space W p has a natural hyper-Kahler structure, and G p acts on W p preserving this structure. The action of G p has a hyper-Kahler moment map µ, which is simply the left hand side of Hitchin's equations.…”

Section: Surface Operators With Wild Ramificationmentioning

confidence: 99%

Gauge Theory and Wild Ramification

Witten

2008

Anal. Appl.

171

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“…Let us gather the generalised eigenspaces appearing in (15) corresponding to equal values of ζ i,j to define a coarser decomposition…”

Section: The Correspondence In the Irregular Casementioning

confidence: 99%

“…Higgs bundles with tame (or regular) singularities compatible with a parabolic structure at the marked points have first been studied by C. Simpson [22]. In [26] K. Yokogawa and in [9] H. Boden and K. Yokogawa constructed a moduli space of parabolic Higgs bundles with regular singularities using Geometric Invariant Theory; parallelly, a gauge-theoretic construction was provided by H. Konno [15]. Later, Higgs bundles with wild (or irregular) singularities endowed with compatible parabolic structures have also been extensively studied from various perspectives in the mathematical literature (see e.g.…”

Section: Introductionmentioning

confidence: 99%