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Holomorphic Higgs bundles over the Teichm\"uller space
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abstract
We study which representations $\rho$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $\Sigma\,=\, (X,\, J)$ via non-abelian Hodge correspondence. For representations $\rho$ into $\mathrm{SL}(2,\mathbb C)$ we show that holomorphic dependency is equivalent to $\rho$ being unitary. For higher ranks this equivalence fails -- we show the existence of non-unitary and irreducible representations of the fundamental group into $\mathrm{SL}(n,\mathbb C)$ admitting Higgs data that are holomorphic in $\Sigma$, for $n$ large enough.
Forward citations
Cited by 3 Pith papers
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Higher order isomonodromic deformation of Higgs bundles and a characterization of the non-abelian Noether-Lefschetz locus
The non-abelian Noether-Lefschetz locus equals the maximal complex analytic subvariety on which the isomonodromic deformation of Higgs bundles is holomorphic.
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Isomonodromic deformations of Higgs bundles and characterization of the non-abelian Noether--Lefschetz locus
Proves equivalence between holomorphicity of isomonodromic Higgs bundle families and isomonodromicity under C*-rescaling, yielding a local characterization of non-abelian Noether-Lefschetz loci.
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A universal Higgs bundle moduli space
A symplectic connection over Teichmüller space, derived from the harmonic-map energy, carries an integrable complex structure that realizes the universal Higgs bundle moduli space and satisfies Higgs-bundle-like curva...
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