Geodesic
Rationality of moduli varieties of plane curves of degree~$3k$
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 375-381

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It is proved that the moduli varieties $\mathfrak A_d$ of plane curves of degree $d\equiv0\mod3$ are rational for sufficiently large $d$. (N. I. Shepherd-Barron has determined and partially realized a method for proving the rationality of the varieties $\mathfrak A_d$.) Bibliography: 3 titles. 
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     author = {P. I. Katsylo},
     title = {Rationality of moduli varieties of plane curves of degree~$3k$},
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     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_2_a5/}
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P. I. Katsylo. Rationality of moduli varieties of plane curves of degree~$3k$. Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 375-381. http://geodesic.mathdoc.fr/item/SM_1989_64_2_a5/