Automorphisms of singular cubic threefolds and the Cremona group
type: Item
instance of: scholarly article
title: Automorphisms of singular cubic threefolds and the Cremona group
zbMATH Open document ID: 1375.14052
DOI: 10.1134/S0001434616090169
author: Artem A. Avilov
published in: Mathematical Notes
publication date: 2017-02-09T00:00:00Z
review text: 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.
reviewed by: Emilia Mezzetti
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 14J50
zbMATH DE Number: 6682259
zbMATH Keywords: variety
zbMATH Keywords: group
zbMATH Keywords: fibration
zbMATH Keywords: hypersurface
MaRDI profile type: Publication
cites work: \(G\)-Fano threefolds. I.
cites work: The intermediate Jacobian of the cubic threefold
description: scientific article; zbMATH DE number 6682259