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