Abstract
It is a folklore theorem that the Kuranishi slice method can be used to
construct the moduli space of semistable Higgs bundles on a closed Riemann
surface as a complex space. The purpose of this paper is to provide a proof in
detail. We also give a direct proof that the moduli space is locally modeled on
an affine GIT quotient of a quadratic cone by a complex reductive group.
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