Geodesic
Rationality of moduli varieties of plane curves of degree $3k$
Sbornik. Mathematics, Tome 64 (1989) no. 2, pp. 375-381 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Bogomolov F. A., Katsylo P. I., “Ratsionalnost nekotorykh faktormnogoobrazii”, Matem. sb., 126(168) (1985), 548–589 | MR

[2] Formanek E., “The center of the ring of 3x3 generic matrices”, Lin. Mult. Alg. Math., 25 (1974), 299–325