  We present the following result: consider the space of complex polynomials of
degree n>2 with n-1 distinct marked periodic orbits of given periods. Then this
space is irreducible and the multipliers of the marked periodic orbits
considered as algebraic functions on the above mentioned space, are
algebraically independent over $\mathbb C$. Equivalently, this means that at
its generic point, the moduli space of degree n polynomial maps can be locally
parameterized by the multipliers of n-1 arbitrary distinct periodic orbits. A
detailed proof of this result (together with a proof of a more general
statement) is given in [arXiv:1305.0867]. In this exposition we substitute some
of the technical lemmas from [arXiv:1305.0867] with more geometric arguments.
