For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in is quasi-projective.
2000 Mathematics Subject Classification: 14Q05, 14Q15, 14R20, 14D22.Let Hg be the moduli space of genus g hyperelliptic curves. In this note, we study the locus Hg (G,σ) in Hg of curves admitting a G-action of given ramification type σ and inclusions between such loci. For each genus we determine the list of all possible groups, the inclusions among the loci, and the corresponding equations of the generic curve in Hg (G, σ). The proof of the results is based solely on representations of finite subgroups...