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On Moduli Space of Higgs GO(m,ℂ) Bundles Over a Riemann Surface
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Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by KX. Let MH denote the moduli space of semi-stable Higgs GO(m,ℂ)-bundles over X of fixed topological type. The complex variety MH has a natural holomorphic symplectic structure. On the other hand, for any d0≥1, the Liouville symplectic form on the total space of KX defines a holomorphic symplectic structure on the Hilbert scheme Hilbd0 (KX) parametrizing the 0-dimensional subschemes of KX. We relate the symplectic form on Hilbd0 (KX) with the symplectic form on MH.
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