  Tikhomirov (2009) proved the irreducibility of the moduli space of
mathematical instantons on the projective 3-space for all odd charges. The
irreducibility for charges between 1 and 5 was known before. In the present
paper, the rationality of the instanton moduli spaces is proved under the
assumption of the irreducibility. So, in particular, the instanton moduli
spaces are rational for all odd charges and for charges 2 and 4.
