Automorphisms of singular cubic threefolds and the Cremona group (Q509149)

The author is interested in describing rational cubic threefolds which are rational Fano \(G\)-varieties, because this problem is related to the study of finite subgroups of the Cremona group. Here he proves that, if \(X\) is a cubic threefold of this type, such that \(G\) is neither linearizable nor of fiber type, then all singularities of \(X\) are ordinary double points. \textit{H. Finkelnberg} and \textit{J. Werner} [Indag. Math. 51, No. 2, 185--198 (1989; Zbl 0703.14026)] gave a classification of cubic threefolds whose singularities are ordinary double points. Using this classification the author is able to prove that then \(X\) belongs to a list of \(6\) possibilities. The author also includes explicit equations of all the 6 examples.