Geodesic
Rationality of the orbit spaces of irreducible representations of the group~$\operatorname{SL}_2$
Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 23-32

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In this paper the rationality of the moduli spaces of hyperelliptic curves of genus $g\geqslant15$ is proved. Bibliography: 6 titles. 
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     author = {P. I. Katsylo},
     title = {Rationality of the orbit spaces of irreducible representations of the group~$\operatorname{SL}_2$},
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P. I. Katsylo. Rationality of the orbit spaces of irreducible representations of the group~$\operatorname{SL}_2$. Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 23-32. http://geodesic.mathdoc.fr/item/IM2_1984_22_1_a1/