Year: 2026
Type: preprint
Abstract: 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 $\mathsf{PSL}_2(\mathbb{F}_{11})$ is $3$. This disproves a conjecture of Dolgachev that the essential dimension of a group is at least its Cremona dimension.
Source: arXiv (Cornell University)
Institutions: University of South Carolina, Columbia University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7220965265