  We show that in the large matrix limit, the eigenvalues of the normal matrix
model for matrices with spectrum inside a compact domain with a special class
of potentials homogeneously fill the interior of a polynomial curve uniquely
defined by the area of its interior domain and its exterior harmonic moments
which are all given as parameters of the potential.
  Then we consider the orthogonal polynomials corresponding to this matrix
model and show that, under certain assumptions, the density of the zeros of the
highest relevant orthogonal polynomial in the large matrix limit is (up to some
constant factor) given by the discontinuity of the Schwarz function of this
polynomial curve.
