Zhi-Jia Zhang

Equivariant Unirationality of Cubic Threefolds

Using the recent proof of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces, we finish the classification of $G$-unirational complex cubic threefolds. In particular, we prove that the Klein cubic threefold is $\mathsf{PSL}_2(\mathbb{F}_{11})$-unirational, establishing that the essential dimension of $\mathsf{P...