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.
Construction of the moduli space of Spin (7)-instantons
A new construction of compact $G_2$-manifolds by gluing families of Eguchi-Hanson spaces
Construction of Maximal Hypersurfaces with Boundary Conditions
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