  There is a canonical isomorphism between the coarse moduli spaces of somooth
hyperelliptic curves of genus g and binary forms of degree 2g+2 with nonzero
discriminant. In this paper, we study the extension of this isomorphism to the
compactification of these moduli spaces. The main result is that the canonical
isomorphism above extends to a holomorphic map f_g from the compactication of
the moduli space of hyperelliptic curves of genus g to the compactification of
the moduli space of binary forms of degree 2g+2. Moreover, we work out how the
boundary components are contracted by the map f_g.
