Projective moduli space for the polynomials

The projective moduli space is defined as the space of all collections of conjugacy classes of polynomial maps that the sum of their degrees equals to n or less. In this paper, we define a map from the projective moduli space to CPn-1 via the elementary symmetric functions of the multipliers at the fixed points. For the case of degree 4, we give the transformation formula, and show that quartic polynomials degenerate into quadratic polynomials on the set called exceptional set.