Abstract
AbstractLet be a compact Kähler manifold and be a Higgs bundle over it. We study the structure of the Kuranishi space for the pair when the Higgs bundle admits a harmonic metric or equivalently when the Higgs bundle is polystable and the Chern classes are 0. Under such assumptions, we show that the Kuranishi space of the pair is isomorphic to the direct product of the Kuranishi space of and the Kuranishi space of . Moreover, when is a Riemann surface and is stable and the degree is 0, we show that the deformation of the pair is unobstructed and calculate the dimension of the Kuranishi space.
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