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Following the author's previous works, we continue to consider the problem ofcounting the number of affine conjugacy classes of polynomials of one complexvariable when its unordered collection of holomorphic fixed point indices isgiven. The problem was already solved completely in the case that thepolynomials have no multiple fixed points, in the author's previous papers. Inthis paper, we consider the case of having multiple fixed points, and obtainthe formulae for generic unordered collections of holomorphic fixed pointindices, for each given degree and for each given number of fixed points.

The Moduli Space of Polynomial Maps and Their Holomorphic Indices: I. Generic Properties in the Case of Having Multiple Fixed Points