An analytic approach to the quasi-projectivity of the moduli space of Higgs bundles

The moduli space of Higgs bundles can be defined as a quotient an infinite-dimensional space. Moreover, by the Kuranishi slice method, it is equipped with structure normal complex In this paper, we will use analytic methods to show that quasi-projective. fact, following Hausel's symplectic cut construct and projective compactification space, hence prove quasi-projectivity. main difference between paper smoothness not assumed.